LMFDB - Embedded newform 1183.2.e.h.170.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1183,2,Mod(170,1183)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1183, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1183.170"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.3
Root			$-0.437442 - 0.757672i$ of defining polynomial
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.h.508.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.134063 - 0.232203i) q^{2} +(0.571504 + 0.989875i) q^{3} +(0.964054 + 1.66979i) q^{4} +(1.28088 - 2.21854i) q^{5} +0.306470 q^{6} +(-2.57801 - 0.594848i) q^{7} +1.05323 q^{8} +(0.846765 - 1.46664i) q^{9} +(-0.343436 - 0.594848i) q^{10} +(-1.97300 - 3.41734i) q^{11} +(-1.10192 + 1.90859i) q^{12} +(-0.483741 + 0.518876i) q^{14} +2.92811 q^{15} +(-1.78691 + 3.09502i) q^{16} +(-0.392550 - 0.679916i) q^{17} +(-0.227039 - 0.393243i) q^{18} +(3.74764 - 6.49110i) q^{19} +4.93934 q^{20} +(-0.884522 - 2.89187i) q^{21} -1.05802 q^{22} +(3.97759 - 6.88938i) q^{23} +(0.601923 + 1.04256i) q^{24} +(-0.781294 - 1.35324i) q^{25} +5.36475 q^{27} +(-1.49207 - 4.87821i) q^{28} +2.35173 q^{29} +(0.392550 - 0.679916i) q^{30} +(1.27718 + 2.21215i) q^{31} +(1.53234 + 2.65409i) q^{32} +(2.25516 - 3.90605i) q^{33} -0.210505 q^{34} +(-4.62182 + 4.95751i) q^{35} +3.26531 q^{36} +(-3.37858 + 5.85187i) q^{37} +(-1.00484 - 1.74043i) q^{38} +(1.34905 - 2.33663i) q^{40} -2.43747 q^{41} +(-0.790083 - 0.182303i) q^{42} -2.24946 q^{43} +(3.80416 - 6.58900i) q^{44} +(-2.16920 - 3.75717i) q^{45} +(-1.06649 - 1.84722i) q^{46} +(-0.658276 + 1.14017i) q^{47} -4.08491 q^{48} +(6.29231 + 3.06705i) q^{49} -0.418969 q^{50} +(0.448688 - 0.777151i) q^{51} +(-4.63977 - 8.03632i) q^{53} +(0.719212 - 1.24571i) q^{54} -10.1087 q^{55} +(-2.71523 - 0.626509i) q^{56} +8.56716 q^{57} +(0.315279 - 0.546079i) q^{58} +(4.48335 + 7.76540i) q^{59} +(2.82286 + 4.88933i) q^{60} +(-4.72273 + 8.18002i) q^{61} +0.684890 q^{62} +(-3.05540 + 3.27732i) q^{63} -6.32592 q^{64} +(-0.604665 - 1.04731i) q^{66} +(0.676281 + 1.17135i) q^{67} +(0.756879 - 1.31095i) q^{68} +9.09284 q^{69} +(0.531538 + 1.73782i) q^{70} +12.3162 q^{71} +(0.891834 - 1.54470i) q^{72} +(-0.384295 - 0.665619i) q^{73} +(0.905882 + 1.56903i) q^{74} +(0.893026 - 1.54677i) q^{75} +14.4517 q^{76} +(3.05363 + 9.98358i) q^{77} +(-3.09642 + 5.36316i) q^{79} +(4.57763 + 7.92868i) q^{80} +(0.525682 + 0.910507i) q^{81} +(-0.326774 + 0.565989i) q^{82} -1.07292 q^{83} +(3.97609 - 4.26489i) q^{84} -2.01123 q^{85} +(-0.301568 + 0.522332i) q^{86} +(1.34402 + 2.32792i) q^{87} +(-2.07801 - 3.59923i) q^{88} +(-3.83149 + 6.63634i) q^{89} -1.16324 q^{90} +15.3384 q^{92} +(-1.45983 + 2.52850i) q^{93} +(0.176501 + 0.305708i) q^{94} +(-9.60052 - 16.6286i) q^{95} +(-1.75148 + 3.03365i) q^{96} -2.37202 q^{97} +(1.55574 - 1.04992i) q^{98} -6.68267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + q^{3} - 4 q^{4} + q^{5} + 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{14} + 4 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} - 9 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + q^3 - 4 * q^4 + q^5 + 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^14 + 4 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 - q^19 + 2 * q^20 - 9 * q^21 + 10 * q^22 - q^23 - 11 * q^24 + 7 * q^25 - 8 * q^27 + 8 * q^28 - 6 * q^29 - 5 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 + 32 * q^34 - 28 * q^35 + 42 * q^36 - 13 * q^37 - 17 * q^38 - 5 * q^40 + 16 * q^41 - 52 * q^42 + 22 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 - 42 * q^48 + 6 * q^49 - 12 * q^50 - 20 * q^51 - 2 * q^53 - 18 * q^54 - 18 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 + 13 * q^59 + 20 * q^60 - 5 * q^61 - 10 * q^62 + 8 * q^63 - 30 * q^64 + 18 * q^66 - 11 * q^67 + 29 * q^68 - 46 * q^69 - 39 * q^70 - 12 * q^71 + 25 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 + 18 * q^76 + 11 * q^77 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 + 41 * q^84 + 2 * q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 + 54 * q^92 - 7 * q^93 + 45 * q^94 - 6 * q^95 + 19 * q^96 + 70 * q^97 - 82 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.134063	−	0.232203i	0.0947966	−	0.164193i	−0.814727	−	0.579845i	$-0.803113\pi$
$2$	0.134063	−	0.232203i	0.0947966	−	0.164193i	0.909524	+	0.415652i	$0.136447\pi$
$3$	0.571504	+	0.989875i	0.329958	+	0.571504i	0.982503	−	0.186246i	$-0.0596320\pi$
$3$	0.571504	+	0.989875i	0.329958	+	0.571504i	−0.652545	+	0.757750i	$0.726299\pi$
$4$	0.964054	+	1.66979i	0.482027	+	0.834896i
$5$	1.28088	−	2.21854i	0.572826	−	0.992163i	−0.423448	−	0.905920i	$-0.639180\pi$
$5$	1.28088	−	2.21854i	0.572826	−	0.992163i	0.996274	−	0.0862431i	$-0.0274862\pi$
$6$	0.306470			0.125116
$7$	−2.57801	−	0.594848i	−0.974398	−	0.224831i
$7$	−2.57801	−	0.594848i	−0.974398	−	0.224831i
$8$	1.05323			0.372371
$9$	0.846765	−	1.46664i	0.282255	−	0.488880i
$10$	−0.343436	−	0.594848i	−0.108604	−	0.188107i
$11$	−1.97300	−	3.41734i	−0.594882	−	1.03037i	−0.993563	−	0.113277i	$-0.963865\pi$
$11$	−1.97300	−	3.41734i	−0.594882	−	1.03037i	0.398681	−	0.917090i	$-0.369468\pi$
$12$	−1.10192	+	1.90859i	−0.318098	+	0.550961i
$13$		0			0
$13$		0			0
$14$	−0.483741	+	0.518876i	−0.129285	+	0.138676i
$15$	2.92811			0.756034
$16$	−1.78691	+	3.09502i	−0.446728	+	0.773755i
$17$	−0.392550	−	0.679916i	−0.0952073	−	0.164904i	0.814488	−	0.580181i	$-0.197018\pi$
$17$	−0.392550	−	0.679916i	−0.0952073	−	0.164904i	−0.909695	+	0.415277i	$0.863685\pi$
$18$	−0.227039	−	0.393243i	−0.0535136	−	0.0926883i
$19$	3.74764	−	6.49110i	0.859767	−	1.48916i	−0.0123849	−	0.999923i	$-0.503942\pi$
$19$	3.74764	−	6.49110i	0.859767	−	1.48916i	0.872151	−	0.489236i	$-0.162724\pi$
$20$	4.93934			1.10447
$21$	−0.884522	−	2.89187i	−0.193018	−	0.631058i
$22$	−1.05802			−0.225571
$23$	3.97759	−	6.88938i	0.829384	−	1.43654i	−0.0691375	−	0.997607i	$-0.522025\pi$
$23$	3.97759	−	6.88938i	0.829384	−	1.43654i	0.898522	−	0.438929i	$-0.144642\pi$
$24$	0.601923	+	1.04256i	0.122867	+	0.212812i
$25$	−0.781294	−	1.35324i	−0.156259	−	0.270648i
$26$		0			0
$27$	5.36475			1.03245
$28$	−1.49207	−	4.87821i	−0.281975	−	0.921895i
$29$	2.35173			0.436705			0.218353	−	0.975870i	$-0.429932\pi$
$29$	2.35173			0.436705			0.218353	+	0.975870i	$0.429932\pi$
$30$	0.392550	−	0.679916i	0.0716695	−	0.124135i
$31$	1.27718	+	2.21215i	0.229389	+	0.397313i	0.957627	−	0.288011i	$-0.0929939\pi$
$31$	1.27718	+	2.21215i	0.229389	+	0.397313i	−0.728238	+	0.685324i	$0.759661\pi$
$32$	1.53234	+	2.65409i	0.270882	+	0.469182i
$33$	2.25516	−	3.90605i	0.392573	−	0.679956i
$34$	−0.210505			−0.0361013
$35$	−4.62182	+	4.95751i	−0.781230	+	0.837973i
$36$	3.26531			0.544219
$37$	−3.37858	+	5.85187i	−0.555435	+	0.962041i	0.442435	+	0.896801i	$0.354115\pi$
$37$	−3.37858	+	5.85187i	−0.555435	+	0.962041i	−0.997870	+	0.0652406i	$0.979219\pi$
$38$	−1.00484	−	1.74043i	−0.163006	−	0.282334i
$39$		0			0
$40$	1.34905	−	2.33663i	0.213304	−	0.369453i
$41$	−2.43747			−0.380669			−0.190335	−	0.981719i	$-0.560957\pi$
$41$	−2.43747			−0.380669			−0.190335	+	0.981719i	$0.560957\pi$
$42$	−0.790083	−	0.182303i	−0.121912	−	0.0281299i
$43$	−2.24946			−0.343039			−0.171520	−	0.985181i	$-0.554868\pi$
$43$	−2.24946			−0.343039			−0.171520	+	0.985181i	$0.554868\pi$
$44$	3.80416	−	6.58900i	0.573499	−	0.993329i
$45$	−2.16920	−	3.75717i	−0.323366	−	0.560086i
$46$	−1.06649	−	1.84722i	−0.157246	−	0.272357i
$47$	−0.658276	+	1.14017i	−0.0960195	+	0.166311i	−0.910034	−	0.414534i	$-0.863944\pi$
$47$	−0.658276	+	1.14017i	−0.0960195	+	0.166311i	0.814014	+	0.580845i	$0.197278\pi$
$48$	−4.08491			−0.589606
$49$	6.29231	+	3.06705i	0.898902	+	0.438150i
$50$	−0.418969			−0.0592512
$51$	0.448688	−	0.777151i	0.0628289	−	0.108823i
$52$		0			0
$53$	−4.63977	−	8.03632i	−0.637321	−	1.10387i	−0.986018	−	0.166637i	$-0.946709\pi$
$53$	−4.63977	−	8.03632i	−0.637321	−	1.10387i	0.348697	−	0.937236i	$-0.386624\pi$
$54$	0.719212	−	1.24571i	0.0978724	−	0.169520i
$55$	−10.1087			−1.36306
$56$	−2.71523	−	0.626509i	−0.362838	−	0.0837207i
$57$	8.56716			1.13475
$58$	0.315279	−	0.546079i	0.0413981	−	0.0717037i
$59$	4.48335	+	7.76540i	0.583683	+	1.01097i	0.995038	+	0.0994935i	$0.0317223\pi$
$59$	4.48335	+	7.76540i	0.583683	+	1.01097i	−0.411355	+	0.911475i	$0.634944\pi$
$60$	2.82286	+	4.88933i	0.364429	+	0.631210i
$61$	−4.72273	+	8.18002i	−0.604684	+	1.04734i	0.387417	+	0.921905i	$0.373367\pi$
$61$	−4.72273	+	8.18002i	−0.604684	+	1.04734i	−0.992101	+	0.125439i	$0.959966\pi$
$62$	0.684890			0.0869811
$63$	−3.05540	+	3.27732i	−0.384944	+	0.412904i
$64$	−6.32592			−0.790741
$65$		0			0
$66$	−0.604665	−	1.04731i	−0.0744291	−	0.128915i
$67$	0.676281	+	1.17135i	0.0826209	+	0.143104i	0.904375	−	0.426739i	$-0.140338\pi$
$67$	0.676281	+	1.17135i	0.0826209	+	0.143104i	−0.821754	+	0.569842i	$0.807004\pi$
$68$	0.756879	−	1.31095i	0.0917851	−	0.158976i
$69$	9.09284			1.09465
$70$	0.531538	+	1.73782i	0.0635309	+	0.207709i
$71$	12.3162			1.46166			0.730829	−	0.682560i	$-0.239133\pi$
$71$	12.3162			1.46166			0.730829	+	0.682560i	$0.239133\pi$
$72$	0.891834	−	1.54470i	0.105104	−	0.182045i
$73$	−0.384295	−	0.665619i	−0.0449783	−	0.0779048i	0.842660	−	0.538446i	$-0.180989\pi$
$73$	−0.384295	−	0.665619i	−0.0449783	−	0.0779048i	−0.887638	+	0.460542i	$0.847655\pi$
$74$	0.905882	+	1.56903i	0.105307	+	0.182396i
$75$	0.893026	−	1.54677i	0.103118	−	0.178605i
$76$	14.4517			1.65772
$77$	3.05363	+	9.98358i	0.347993	+	1.13773i
$78$		0			0
$79$	−3.09642	+	5.36316i	−0.348375	+	0.603402i	−0.985961	−	0.166976i	$-0.946600\pi$
$79$	−3.09642	+	5.36316i	−0.348375	+	0.603402i	0.637586	+	0.770379i	$0.279933\pi$
$80$	4.57763	+	7.92868i	0.511794	+	0.886454i
$81$	0.525682	+	0.910507i	0.0584091	+	0.101167i
$82$	−0.326774	+	0.565989i	−0.0360861	+	0.0625030i
$83$	−1.07292			−0.117768			−0.0588841	−	0.998265i	$-0.518754\pi$
$83$	−1.07292			−0.117768			−0.0588841	+	0.998265i	$0.518754\pi$
$84$	3.97609	−	4.26489i	0.433827	−	0.465337i
$85$	−2.01123			−0.218149
$86$	−0.301568	+	0.522332i	−0.0325190	+	0.0563245i
$87$	1.34402	+	2.32792i	0.144094	+	0.249579i
$88$	−2.07801	−	3.59923i	−0.221517	−	0.383679i
$89$	−3.83149	+	6.63634i	−0.406138	+	0.703451i	−0.994453	−	0.105180i	$-0.966458\pi$
$89$	−3.83149	+	6.63634i	−0.406138	+	0.703451i	0.588316	+	0.808631i	$0.299791\pi$
$90$	−1.16324			−0.122616
$91$		0			0
$92$	15.3384			1.59914
$93$	−1.45983	+	2.52850i	−0.151378	+	0.262194i
$94$	0.176501	+	0.305708i	0.0182046	+	0.0315314i
$95$	−9.60052	−	16.6286i	−0.984993	−	1.70606i
$96$	−1.75148	+	3.03365i	−0.178760	+	0.309621i
$97$	−2.37202			−0.240842			−0.120421	−	0.992723i	$-0.538424\pi$
$97$	−2.37202			−0.240842			−0.120421	+	0.992723i	$0.538424\pi$
$98$	1.55574	−	1.04992i	0.157154	−	0.106058i
$99$	−6.68267			−0.671634
$100$	1.50642	−	2.60920i	0.150642	−	0.260920i
$101$	0.398665	+	0.690508i	0.0396686	+	0.0687081i	0.885178	−	0.465252i	$-0.154036\pi$
$101$	0.398665	+	0.690508i	0.0396686	+	0.0687081i	−0.845509	+	0.533961i	$0.820703\pi$
$102$	−0.120305	−	0.208374i	−0.0119119	−	0.0206321i
$103$	−1.08309	+	1.87597i	−0.106720	+	0.184844i	−0.914440	−	0.404722i	$-0.867368\pi$
$103$	−1.08309	+	1.87597i	−0.106720	+	0.184844i	0.807720	+	0.589567i	$0.200701\pi$
$104$		0			0
$105$	−7.54871	−	1.74178i	−0.736678	−	0.169980i
$106$	−2.48808			−0.241664
$107$	5.76311	−	9.98201i	0.557141	−	0.964997i	−0.440592	−	0.897707i	$-0.645232\pi$
$107$	5.76311	−	9.98201i	0.557141	−	0.964997i	0.997733	−	0.0672896i	$-0.0214351\pi$
$108$	5.17191	+	8.95801i	0.497667	+	0.861985i
$109$	−4.03912	−	6.99595i	−0.386877	−	0.670091i	0.605151	−	0.796111i	$-0.293113\pi$
$109$	−4.03912	−	6.99595i	−0.386877	−	0.670091i	−0.992028	+	0.126020i	$0.959780\pi$
$110$	−1.35520	+	2.34727i	−0.129213	+	0.223803i
$111$	−7.72349			−0.733081
$112$	6.44775	−	6.91607i	0.609255	−	0.653507i
$113$	8.04135			0.756467			0.378233	−	0.925710i	$-0.376532\pi$
$113$	8.04135			0.756467			0.378233	+	0.925710i	$0.376532\pi$
$114$	1.14854	−	1.98932i	0.107570	−	0.186317i
$115$	−10.1896	−	17.6489i	−0.950186	−	1.64577i
$116$	2.26719	+	3.92690i	0.210504	+	0.364603i
$117$		0			0
$118$	2.40420			0.221325
$119$	0.607552	+	1.98634i	0.0556942	+	0.182088i
$120$	3.08396			0.281526
$121$	−2.28546	+	3.95854i	−0.207769	+	0.359867i
$122$	1.26628	+	2.19327i	0.114644	+	0.198569i
$123$	−1.39303	−	2.41279i	−0.125605	−	0.217554i
$124$	−2.46255	+	4.26526i	−0.221143	+	0.383032i
$125$	8.80581			0.787615
$126$	0.351390	+	1.14884i	0.0313043	+	0.102347i
$127$	1.78805			0.158663			0.0793317	−	0.996848i	$-0.474721\pi$
$127$	1.78805			0.158663			0.0793317	+	0.996848i	$0.474721\pi$
$128$	−3.91275	+	6.77709i	−0.345842	+	0.599015i
$129$	−1.28558	−	2.22668i	−0.113189	−	0.196049i
$130$		0			0
$131$	3.19545	−	5.53469i	0.279188	−	0.483568i	−0.691995	−	0.721902i	$-0.743268\pi$
$131$	3.19545	−	5.53469i	0.279188	−	0.483568i	0.971183	+	0.238334i	$0.0766014\pi$
$132$	8.69638			0.756923
$133$	−13.5227	+	14.5049i	−1.17256	+	1.25773i
$134$	0.362656			0.0313287
$135$	6.87158	−	11.9019i	0.591412	−	1.02436i
$136$	−0.413443	−	0.716105i	−0.0354525	−	0.0614055i
$137$	−5.01827	−	8.69190i	−0.428740	−	0.742599i	0.568022	−	0.823014i	$-0.307709\pi$
$137$	−5.01827	−	8.69190i	−0.428740	−	0.742599i	−0.996762	+	0.0804144i	$0.974376\pi$
$138$	1.21901	−	2.11139i	0.103769	−	0.179733i
$139$	−5.54557			−0.470369			−0.235184	−	0.971951i	$-0.575569\pi$
$139$	−5.54557			−0.470369			−0.235184	+	0.971951i	$0.575569\pi$
$140$	−12.7337	−	2.93816i	−1.07619	−	0.248320i
$141$	−1.50483			−0.126730
$142$	1.65114	−	2.85985i	0.138560	−	0.239993i
$143$		0			0
$144$	3.02619	+	5.24151i	0.252182	+	0.436793i
$145$	3.01228	−	5.21742i	0.250156	−	0.433283i
$146$	−0.206078			−0.0170552
$147$	0.560087	+	7.98144i	0.0461952	+	0.658298i
$148$	−13.0285			−1.07094
$149$	−9.23254	+	15.9912i	−0.756359	+	1.31005i	0.188337	+	0.982104i	$0.439690\pi$
$149$	−9.23254	+	15.9912i	−0.756359	+	1.31005i	−0.944696	+	0.327947i	$0.893643\pi$
$150$	−0.239443	−	0.414727i	−0.0195504	−	0.0338623i
$151$	−0.803678	−	1.39201i	−0.0654024	−	0.113280i	0.831470	−	0.555570i	$-0.187500\pi$
$151$	−0.803678	−	1.39201i	−0.0654024	−	0.113280i	−0.896872	+	0.442289i	$0.854166\pi$
$152$	3.94710	−	6.83658i	0.320152	−	0.554520i
$153$	−1.32959			−0.107491
$154$	2.72760	+	0.629362i	0.219796	+	0.0507155i
$155$	6.54366			0.525600
$156$		0			0
$157$	0.822967	+	1.42542i	0.0656799	+	0.113761i	0.896995	−	0.442040i	$-0.145745\pi$
$157$	0.822967	+	1.42542i	0.0656799	+	0.113761i	−0.831315	+	0.555801i	$0.812412\pi$
$158$	0.830229	+	1.43800i	0.0660494	+	0.114401i
$159$	5.30330	−	9.18558i	0.420579	−	0.728464i
$160$	7.85096			0.620673
$161$	−14.3524	+	15.3949i	−1.13113	+	1.21329i
$162$	0.281897			0.0221479
$163$	3.27409	−	5.67090i	0.256447	−	0.444179i	−0.708841	−	0.705369i	$-0.750782\pi$
$163$	3.27409	−	5.67090i	0.256447	−	0.444179i	0.965287	+	0.261190i	$0.0841148\pi$
$164$	−2.34986	−	4.07007i	−0.183493	−	0.317819i
$165$	−5.77716	−	10.0063i	−0.449751	−	0.778992i
$166$	−0.143838	+	0.249135i	−0.0111640	+	0.0193367i
$167$	9.54880			0.738908			0.369454	−	0.929249i	$-0.379545\pi$
$167$	9.54880			0.738908			0.369454	+	0.929249i	$0.379545\pi$
$168$	−0.931600	−	3.04579i	−0.0718745	−	0.234988i
$169$		0			0
$170$	−0.269631	+	0.467015i	−0.0206798	+	0.0358184i
$171$	−6.34673	−	10.9929i	−0.485347	−	0.840646i
$172$	−2.16860	−	3.75613i	−0.165354	−	0.286402i
$173$	−5.56582	+	9.64028i	−0.423161	+	0.732937i	−0.996247	−	0.0865588i	$-0.972413\pi$
$173$	−5.56582	+	9.64028i	−0.423161	+	0.732937i	0.573085	+	0.819496i	$0.305746\pi$
$174$	0.720733			0.0546386
$175$	1.20921	+	3.95343i	0.0914080	+	0.298851i
$176$	14.1023			1.06300
$177$	−5.12451	+	8.87592i	−0.385182	+	0.667155i
$178$	1.02732	+	1.77937i	0.0770009	+	0.133369i
$179$	6.32173	+	10.9496i	0.472508	+	0.818409i	0.999505	−	0.0314588i	$-0.0100153\pi$
$179$	6.32173	+	10.9496i	0.472508	+	0.818409i	−0.526997	+	0.849867i	$0.676682\pi$
$180$	4.18246	−	7.24424i	0.311742	−	0.539954i
$181$	14.9158			1.10868			0.554341	−	0.832289i	$-0.312970\pi$
$181$	14.9158			1.10868			0.554341	+	0.832289i	$0.312970\pi$
$182$		0			0
$183$	−10.7963			−0.798082
$184$	4.18930	−	7.25607i	0.308839	−	0.534925i
$185$	8.65509	+	14.9911i	0.636335	+	1.10216i
$186$	0.391418	+	0.677956i	0.0287001	+	0.0497101i
$187$	−1.54900	+	2.68295i	−0.113274	+	0.196197i
$188$	−2.53846			−0.185136
$189$	−13.8304	−	3.19121i	−1.00601	−	0.232126i
$190$	−5.14829			−0.373496
$191$	7.06528	−	12.2374i	0.511226	−	0.885469i	−0.488690	−	0.872458i	$-0.662525\pi$
$191$	7.06528	−	12.2374i	0.511226	−	0.885469i	0.999915	−	0.0130110i	$-0.00414165\pi$
$192$	−3.61529	−	6.26187i	−0.260911	−	0.451912i
$193$	−1.94727	−	3.37277i	−0.140167	−	0.242777i	0.787392	−	0.616452i	$-0.211431\pi$
$193$	−1.94727	−	3.37277i	−0.140167	−	0.242777i	−0.927560	+	0.373675i	$0.878097\pi$
$194$	−0.317999	+	0.550790i	−0.0228310	+	0.0395444i
$195$		0			0
$196$	0.944795	+	13.4637i	0.0674853	+	0.961689i
$197$	−11.7089			−0.834224			−0.417112	−	0.908855i	$-0.636958\pi$
$197$	−11.7089			−0.834224			−0.417112	+	0.908855i	$0.636958\pi$
$198$	−0.895897	+	1.55174i	−0.0636686	+	0.110277i
$199$	−1.74842	−	3.02835i	−0.123942	−	0.214674i	0.797377	−	0.603482i	$-0.206220\pi$
$199$	−1.74842	−	3.02835i	−0.123942	−	0.214674i	−0.921319	+	0.388808i	$0.872887\pi$
$200$	−0.822878	−	1.42527i	−0.0581863	−	0.100782i
$201$	−0.772995	+	1.33887i	−0.0545229	+	0.0944364i
$202$	0.213784			0.0150418
$203$	−6.06279	−	1.39892i	−0.425524	−	0.0981850i
$204$	1.73024			0.121141
$205$	−3.12210	+	5.40764i	−0.218057	+	0.377686i
$206$	0.290403	+	0.502994i	0.0202334	+	0.0350452i
$207$	−6.73617	−	11.6674i	−0.468196	−	0.810939i
$208$		0			0
$209$	−29.5764			−2.04584
$210$	−1.41645	+	1.51933i	−0.0977441	+	0.104843i
$211$	19.0052			1.30837			0.654184	−	0.756335i	$-0.273012\pi$
$211$	19.0052			1.30837			0.654184	+	0.756335i	$0.273012\pi$
$212$	8.94598	−	15.4949i	0.614412	−	1.06419i
$213$	7.03874	+	12.1915i	0.482286	+	0.835345i
$214$	−1.54524	−	2.67643i	−0.105630	−	0.182957i
$215$	−2.88128	+	4.99053i	−0.196502	+	0.340351i
$216$	5.65029			0.384453
$217$	−1.97671	−	6.46267i	−0.134188	−	0.438715i
$218$	−2.16598			−0.146698
$219$	0.439253	−	0.760808i	0.0296820	−	0.0514106i
$220$	−9.74533	−	16.8794i	−0.657030	−	1.13801i
$221$		0			0
$222$	−1.03543	+	1.79342i	−0.0694936	+	0.120366i
$223$	−11.9662			−0.801317			−0.400658	−	0.916228i	$-0.631219\pi$
$223$	−11.9662			−0.801317			−0.400658	+	0.916228i	$0.631219\pi$
$224$	−2.37162	−	7.75380i	−0.158460	−	0.518072i
$225$	−2.64629			−0.176419
$226$	1.07804	−	1.86723i	0.0717104	−	0.124206i
$227$	−7.69209	−	13.3231i	−0.510542	−	0.884284i	−0.999925	−	0.0122157i	$-0.996112\pi$
$227$	−7.69209	−	13.3231i	−0.510542	−	0.884284i	0.489384	−	0.872069i	$-0.337222\pi$
$228$	8.25921	+	14.3054i	0.546980	+	0.947396i
$229$	−4.33084	+	7.50123i	−0.286190	+	0.495695i	−0.972897	−	0.231239i	$-0.925722\pi$
$229$	−4.33084	+	7.50123i	−0.286190	+	0.495695i	0.686707	+	0.726934i	$0.259055\pi$
$230$	−5.46418			−0.360297
$231$	−8.13733	+	8.72837i	−0.535397	+	0.574285i
$232$	2.47690			0.162616
$233$	−10.1253	+	17.5376i	−0.663333	+	1.14893i	0.316402	+	0.948625i	$0.397525\pi$
$233$	−10.1253	+	17.5376i	−0.663333	+	1.14893i	−0.979734	+	0.200301i	$0.935808\pi$
$234$		0			0
$235$	1.68634	+	2.92083i	0.110005	+	0.190534i
$236$	−8.64440	+	14.9725i	−0.562702	+	0.974629i
$237$	−7.07847			−0.459796
$238$	0.542685	+	0.125218i	0.0351770	+	0.00811671i
$239$	16.5526			1.07070			0.535350	−	0.844630i	$-0.320180\pi$
$239$	16.5526			1.07070			0.535350	+	0.844630i	$0.320180\pi$
$240$	−5.23227	+	9.06256i	−0.337742	+	0.584985i
$241$	8.20038	+	14.2035i	0.528233	+	0.914926i	0.999458	+	0.0329132i	$0.0104785\pi$
$241$	8.20038	+	14.2035i	0.528233	+	0.914926i	−0.471225	+	0.882013i	$0.656188\pi$
$242$	0.612791	+	1.06138i	0.0393917	+	0.0682284i
$243$	7.44626	−	12.8973i	0.477678	−	0.827362i
$244$	−18.2119			−1.16590
$245$	14.8641	−	10.0313i	0.949631	−	0.640874i
$246$	−0.747011			−0.0476277
$247$		0			0
$248$	1.34516	+	2.32989i	0.0854178	+	0.147948i
$249$	−0.613178	−	1.06206i	−0.0388586	−	0.0673051i
$250$	1.18053	−	2.04474i	0.0746632	−	0.129321i
$251$	−20.4307			−1.28958			−0.644788	−	0.764362i	$-0.723054\pi$
$251$	−20.4307			−1.28958			−0.644788	+	0.764362i	$0.723054\pi$
$252$	−8.41802	−	1.94236i	−0.530285	−	0.122357i
$253$	−31.3911			−1.97354
$254$	0.239710	−	0.415190i	0.0150407	−	0.0260513i
$255$	−1.14943	−	1.99087i	−0.0719800	−	0.124673i
$256$	−5.27682	−	9.13972i	−0.329801	−	0.571232i
$257$	−6.88895	+	11.9320i	−0.429721	+	0.744299i	−0.996848	−	0.0793315i	$-0.974721\pi$
$257$	−6.88895	+	11.9320i	−0.429721	+	0.744299i	0.567127	+	0.823630i	$0.308055\pi$
$258$	−0.689391			−0.0429196
$259$	12.1910	−	13.0765i	0.757511	−	0.812532i
$260$		0			0
$261$	1.99136	−	3.44914i	0.123262	−	0.213496i
$262$	−0.856782	−	1.48399i	−0.0529321	−	0.0916812i
$263$	−12.9587	−	22.4451i	−0.799065	−	1.38402i	−0.920225	−	0.391389i	$-0.871995\pi$
$263$	−12.9587	−	22.4451i	−0.799065	−	1.38402i	0.121160	−	0.992633i	$-0.461338\pi$
$264$	2.37519	−	4.11395i	0.146183	−	0.253196i
$265$	−23.7719			−1.46030
$266$	1.55519	+	5.08457i	0.0953549	+	0.311755i
$267$	−8.75887			−0.536034
$268$	−1.30394	+	2.25850i	−0.0796510	+	0.137960i
$269$	15.0333	+	26.0384i	0.916596	+	1.58759i	0.804547	+	0.593889i	$0.202408\pi$
$269$	15.0333	+	26.0384i	0.916596	+	1.58759i	0.112050	+	0.993703i	$0.464258\pi$
$270$	−1.84245	−	3.19121i	−0.112128	−	0.194211i
$271$	−7.22527	+	12.5145i	−0.438904	+	0.760204i	−0.997605	−	0.0691651i	$-0.977966\pi$
$271$	−7.22527	+	12.5145i	−0.438904	+	0.760204i	0.558701	+	0.829369i	$0.311300\pi$
$272$	2.80581			0.170127
$273$		0			0
$274$	−2.69105			−0.162572
$275$	−3.08299	+	5.33989i	−0.185911	+	0.322008i
$276$	8.76599	+	15.1831i	0.527651	+	0.913918i
$277$	7.66274	+	13.2723i	0.460409	+	0.797452i	0.998981	−	0.0451272i	$-0.0143693\pi$
$277$	7.66274	+	13.2723i	0.460409	+	0.797452i	−0.538572	+	0.842580i	$0.681036\pi$
$278$	−0.743453	+	1.28770i	−0.0445894	+	0.0772310i
$279$	4.32590			0.258985
$280$	−4.86781	+	5.22138i	−0.290907	+	0.312037i
$281$	5.29279			0.315741			0.157871	−	0.987460i	$-0.449537\pi$
$281$	5.29279			0.315741			0.157871	+	0.987460i	$0.449537\pi$
$282$	−0.201742	+	0.349427i	−0.0120135	+	0.0208081i
$283$	15.3923	+	26.6602i	0.914975	+	1.58478i	0.806938	+	0.590636i	$0.201123\pi$
$283$	15.3923	+	26.6602i	0.914975	+	1.58478i	0.108036	+	0.994147i	$0.465544\pi$
$284$	11.8734	+	20.5654i	0.704559	+	1.22033i
$285$	10.9735	−	19.0066i	0.650013	−	1.12586i
$286$		0			0
$287$	6.28384	+	1.44992i	0.370923	+	0.0855864i
$288$	5.19013			0.305831
$289$	8.19181	−	14.1886i	0.481871	−	0.834625i
$290$	−0.807667	−	1.39892i	−0.0474279	−	0.0821474i
$291$	−1.35562	−	2.34800i	−0.0794677	−	0.137642i
$292$	0.740963	−	1.28339i	0.0433616	−	0.0751044i
$293$	−17.5173			−1.02337			−0.511685	−	0.859173i	$-0.670979\pi$
$293$	−17.5173			−1.02337			−0.511685	+	0.859173i	$0.670979\pi$
$294$	1.92840	+	0.939958i	0.112467	+	0.0548195i
$295$	22.9705			1.33739
$296$	−3.55840	+	6.16333i	−0.206828	+	0.358237i
$297$	−10.5847	−	18.3332i	−0.614184	−	1.06380i
$298$	2.47548	+	4.28765i	0.143400	+	0.248377i
$299$		0			0
$300$	3.44370			0.198822
$301$	5.79914	+	1.33809i	0.334257	+	0.0771260i
$302$	−0.430973			−0.0247997
$303$	−0.455678	+	0.789257i	−0.0261780	+	0.0453416i
$304$	13.3934	+	23.1980i	0.768163	+	1.33050i
$305$	12.0985	+	20.9552i	0.692757	+	1.19989i
$306$	−0.178248	+	0.308735i	−0.0101898	+	0.0176492i
$307$	−8.63573			−0.492867			−0.246434	−	0.969160i	$-0.579259\pi$
$307$	−8.63573			−0.492867			−0.246434	+	0.969160i	$0.579259\pi$
$308$	−13.7266	+	14.7236i	−0.782147	+	0.838957i
$309$	−2.47596			−0.140852
$310$	0.877260	−	1.51946i	0.0498250	−	0.0862995i
$311$	8.21130	+	14.2224i	0.465620	+	0.806478i	0.999229	−	0.0392535i	$-0.0124980\pi$
$311$	8.21130	+	14.2224i	0.465620	+	0.806478i	−0.533609	+	0.845731i	$0.679165\pi$
$312$		0			0
$313$	−5.02308	+	8.70024i	−0.283921	+	0.491766i	−0.972347	−	0.233541i	$-0.924969\pi$
$313$	−5.02308	+	8.70024i	−0.283921	+	0.491766i	0.688426	+	0.725307i	$0.258302\pi$
$314$	0.441316			0.0249049
$315$	3.35729	+	10.9764i	0.189162	+	0.618450i
$316$	−11.9405			−0.671704
$317$	−5.07249	+	8.78581i	−0.284899	+	0.493460i	−0.972585	−	0.232549i	$-0.925294\pi$
$317$	−5.07249	+	8.78581i	−0.284899	+	0.493460i	0.687685	+	0.726009i	$0.258627\pi$
$318$	−1.42195	−	2.46289i	−0.0797389	−	0.138112i
$319$	−4.63996	−	8.03665i	−0.259788	−	0.449966i
$320$	−8.10273	+	14.0343i	−0.452957	+	0.784544i
$321$	13.1746			0.735333
$322$	1.65062	+	5.39655i	0.0919853	+	0.300738i
$323$	−5.88454			−0.327424
$324$	−1.01357	+	1.75556i	−0.0563095	+	0.0975310i
$325$		0			0
$326$	−0.877867	−	1.52051i	−0.0486206	−	0.0842133i
$327$	4.61674	−	7.99644i	0.255307	−	0.442204i
$328$	−2.56721			−0.141750
$329$	2.37527	−	2.54780i	0.130953	−	0.140464i
$330$	−3.09801			−0.170540
$331$	−1.15958	+	2.00845i	−0.0637363	+	0.110395i	−0.896133	−	0.443786i	$-0.853635\pi$
$331$	−1.15958	+	2.00845i	−0.0637363	+	0.110395i	0.832396	+	0.554181i	$0.186968\pi$
$332$	−1.03435	−	1.79155i	−0.0567675	−	0.0983242i
$333$	5.72172	+	9.91032i	0.313549	+	0.543082i
$334$	1.28014	−	2.21726i	0.0700460	−	0.121323i
$335$	3.46493			0.189309
$336$	10.5310	+	2.42990i	0.574511	+	0.132562i
$337$	−15.9998			−0.871565			−0.435783	−	0.900052i	$-0.643528\pi$
$337$	−15.9998			−0.871565			−0.435783	+	0.900052i	$0.643528\pi$
$338$		0			0
$339$	4.59567	+	7.95993i	0.249602	+	0.432324i
$340$	−1.93894	−	3.35834i	−0.105154	−	0.182132i
$341$	5.03977	−	8.72913i	0.272919	−	0.472709i
$342$	−3.40344			−0.184037
$343$	−14.3972	−	11.6499i	−0.777378	−	0.629034i
$344$	−2.36919			−0.127738
$345$	11.6468	−	20.1729i	0.627043	−	1.08607i
$346$	1.49234	+	2.58480i	0.0802285	+	0.138960i
$347$	11.4104	+	19.7634i	0.612543	+	1.06096i	0.990810	+	0.135259i	$0.0431867\pi$
$347$	11.4104	+	19.7634i	0.612543	+	1.06096i	−0.378267	+	0.925696i	$0.623480\pi$
$348$	−2.59142	+	4.48848i	−0.138915	+	0.240608i
$349$	−22.7022			−1.21522			−0.607612	−	0.794234i	$-0.707872\pi$
$349$	−22.7022			−1.21522			−0.607612	+	0.794234i	$0.707872\pi$
$350$	1.08011	+	0.249223i	0.0577342	+	0.0133215i
$351$		0			0
$352$	6.04662	−	10.4731i	0.322286	−	0.558216i
$353$	13.6322	+	23.6116i	0.725568	+	1.25672i	0.958740	+	0.284286i	$0.0917564\pi$
$353$	13.6322	+	23.6116i	0.725568	+	1.25672i	−0.233171	+	0.972436i	$0.574910\pi$
$354$	1.37401	+	2.37986i	0.0730279	+	0.126488i
$355$	15.7755	−	27.3239i	0.837276	−	1.45020i
$356$	−14.7751			−0.783077
$357$	−1.61901	+	1.73660i	−0.0856871	+	0.0919108i
$358$	3.39003			0.179169
$359$	7.21309	−	12.4934i	0.380692	−	0.659378i	−0.610469	−	0.792040i	$-0.709019\pi$
$359$	7.21309	−	12.4934i	0.380692	−	0.659378i	0.991161	+	0.132662i	$0.0423524\pi$
$360$	−2.28466	−	3.95715i	−0.120412	−	0.208560i
$361$	−18.5895	−	32.1980i	−0.978397	−	1.69463i
$362$	1.99965	−	3.46350i	0.105099	−	0.182037i
$363$	−5.22461			−0.274221
$364$		0			0
$365$	−1.96894			−0.103059
$366$	−1.44737	+	2.50693i	−0.0756555	+	0.131039i
$367$	5.69586	+	9.86553i	0.297322	+	0.514976i	0.975522	−	0.219901i	$-0.0705733\pi$
$367$	5.69586	+	9.86553i	0.297322	+	0.514976i	−0.678201	+	0.734877i	$0.737240\pi$
$368$	14.2152	+	24.6214i	0.741018	+	1.28348i
$369$	−2.06397	+	3.57489i	−0.107446	+	0.186102i
$370$	4.64130			0.241289
$371$	7.18100	+	23.4777i	0.372819	+	1.21890i
$372$	−5.62943			−0.291872
$373$	15.4815	−	26.8147i	0.801599	−	1.38841i	−0.116964	−	0.993136i	$-0.537316\pi$
$373$	15.4815	−	26.8147i	0.801599	−	1.38841i	0.918563	−	0.395274i	$-0.129351\pi$
$374$	0.415327	+	0.719367i	0.0214760	+	0.0371976i
$375$	5.03256	+	8.71665i	0.259880	+	0.450126i
$376$	−0.693313	+	1.20085i	−0.0357549	+	0.0619293i
$377$		0			0
$378$	−2.59515	+	2.78364i	−0.133480	+	0.143175i
$379$	10.5866			0.543797			0.271898	−	0.962326i	$-0.412349\pi$
$379$	10.5866			0.543797			0.271898	+	0.962326i	$0.412349\pi$
$380$	18.5109	−	32.0617i	0.949587	−	1.64473i
$381$	1.02188	+	1.76994i	0.0523523	+	0.0906768i
$382$	−1.89438	−	3.28116i	−0.0969249	−	0.167879i
$383$	−15.3758	+	26.6317i	−0.785668	+	1.36082i	0.142931	+	0.989733i	$0.454347\pi$
$383$	−15.3758	+	26.6317i	−0.785668	+	1.36082i	−0.928599	+	0.371084i	$0.878986\pi$
$384$	−8.94462			−0.456453
$385$	26.0603	+	6.01313i	1.32816	+	0.306458i
$386$	−1.04422			−0.0531496
$387$	−1.90476	+	3.29915i	−0.0968246	+	0.167705i
$388$	−2.28675	−	3.96077i	−0.116092	−	0.201078i
$389$	8.18978	+	14.1851i	0.415239	+	0.719214i	0.995453	−	0.0952492i	$-0.0303648\pi$
$389$	8.18978	+	14.1851i	0.415239	+	0.719214i	−0.580215	+	0.814463i	$0.697031\pi$
$390$		0			0
$391$	−6.24561			−0.315854
$392$	6.62722	+	3.23030i	0.334725	+	0.163155i
$393$	7.30486			0.368482
$394$	−1.56972	+	2.71884i	−0.0790816	+	0.136973i
$395$	7.93227	+	13.7391i	0.399116	+	0.691289i
$396$	−6.44246	−	11.1587i	−0.323746	−	0.560744i
$397$	7.94133	−	13.7548i	0.398564	−	0.690333i	−0.594985	−	0.803737i	$-0.702842\pi$
$397$	7.94133	−	13.7548i	0.398564	−	0.690333i	0.993549	+	0.113404i	$0.0361755\pi$
$398$	−0.937591			−0.0469972
$399$	−22.0863	−	5.09616i	−1.10570	−	0.255127i
$400$	5.58441			0.279221
$401$	−3.31787	+	5.74671i	−0.165686	+	0.286977i	−0.936899	−	0.349601i	$-0.886317\pi$
$401$	−3.31787	+	5.74671i	−0.165686	+	0.286977i	0.771212	+	0.636578i	$0.219651\pi$
$402$	0.207259	+	0.358984i	0.0103372	+	0.0179045i
$403$		0			0
$404$	−0.768670	+	1.33137i	−0.0382427	+	0.0662384i
$405$	2.69334			0.133833
$406$	−1.13763	+	1.22026i	−0.0564595	+	0.0605603i
$407$	26.6637			1.32167
$408$	0.472570	−	0.818515i	0.0233957	−	0.0405225i
$409$	−2.93617	−	5.08560i	−0.145184	−	0.251467i	0.784257	−	0.620436i	$-0.213044\pi$
$409$	−2.93617	−	5.08560i	−0.145184	−	0.251467i	−0.929442	+	0.368969i	$0.879711\pi$
$410$	0.837115	+	1.44992i	0.0413421	+	0.0716067i
$411$	5.73593	−	9.93492i	0.282933	−	0.490053i
$412$	−4.17663			−0.205768
$413$	−6.93892	−	22.6862i	−0.341442	−	1.11632i
$414$	−3.61227			−0.177533
$415$	−1.37428	+	2.38032i	−0.0674607	+	0.116845i
$416$		0			0
$417$	−3.16932	−	5.48942i	−0.155202	−	0.268818i
$418$	−3.96508	+	6.86773i	−0.193939	+	0.335911i
$419$	−30.1423			−1.47255			−0.736274	−	0.676683i	$-0.763417\pi$
$419$	−30.1423			−1.47255			−0.736274	+	0.676683i	$0.763417\pi$
$420$	−4.36896	−	14.2839i	−0.213183	−	0.696985i
$421$	40.0580			1.95231			0.976153	−	0.217083i	$-0.0696543\pi$
$421$	40.0580			1.95231			0.976153	+	0.217083i	$0.0696543\pi$
$422$	2.54788	−	4.41306i	0.124029	−	0.214824i
$423$	1.11481	+	1.93091i	0.0542040	+	0.0938840i
$424$	−4.88672	−	8.46405i	−0.237320	−	0.411051i
$425$	−0.613394	+	1.06243i	−0.0297540	+	0.0515354i
$426$	3.77453			0.182876
$427$	17.0411	−	18.2789i	0.824679	−	0.884577i
$428$	22.2238			1.07423
$429$		0			0
$430$	0.772544	+	1.33809i	0.0372554	+	0.0645282i
$431$	1.95793	+	3.39124i	0.0943104	+	0.163350i	0.909321	−	0.416096i	$-0.136602\pi$
$431$	1.95793	+	3.39124i	0.0943104	+	0.163350i	−0.815010	+	0.579447i	$0.803269\pi$
$432$	−9.58632	+	16.6040i	−0.461222	+	0.798860i
$433$	−40.7925			−1.96036			−0.980182	−	0.198100i	$-0.936523\pi$
$433$	−40.7925			−1.96036			−0.980182	+	0.198100i	$0.936523\pi$
$434$	−1.76566	−	0.407405i	−0.0847542	−	0.0195561i
$435$	6.88612			0.330164
$436$	7.78785	−	13.4890i	0.372971	−	0.646004i
$437$	−29.8131	−	51.6378i	−1.42615	−	2.47017i
$438$	−0.117775	−	0.203992i	−0.00562750	−	0.00974711i
$439$	12.7811	−	22.1376i	0.610010	−	1.05657i	−0.381228	−	0.924481i	$-0.624499\pi$
$439$	12.7811	−	22.1376i	0.610010	−	1.05657i	0.991238	−	0.132087i	$-0.0421680\pi$
$440$	−10.6467			−0.507563
$441$	9.82637	−	6.63149i	0.467923	−	0.315785i
$442$		0			0
$443$	13.7282	−	23.7779i	0.652247	−	1.12972i	−0.330330	−	0.943866i	$-0.607160\pi$
$443$	13.7282	−	23.7779i	0.652247	−	1.12972i	0.982576	−	0.185859i	$-0.0595067\pi$
$444$	−7.44586	−	12.8966i	−0.353365	−	0.612046i
$445$	9.81535	+	17.0007i	0.465292	+	0.805910i
$446$	−1.60422	+	2.77859i	−0.0759621	+	0.131570i
$447$	−21.1057			−0.998267
$448$	16.3083	+	3.76296i	0.770496	+	0.177783i
$449$	−14.8036			−0.698626			−0.349313	−	0.937006i	$-0.613585\pi$
$449$	−14.8036			−0.698626			−0.349313	+	0.937006i	$0.613585\pi$
$450$	−0.354769	+	0.614477i	−0.0167240	+	0.0289667i
$451$	4.80913	+	8.32966i	0.226453	+	0.392229i
$452$	7.75230	+	13.4274i	0.364637	+	0.631571i
$453$	0.918611	−	1.59108i	0.0431601	−	0.0747555i
$454$	−4.12489			−0.193590
$455$		0			0
$456$	9.02315			0.422548
$457$	0.325975	−	0.564606i	0.0152485	−	0.0264112i	−0.858300	−	0.513147i	$-0.828479\pi$
$457$	0.325975	−	0.564606i	0.0152485	−	0.0264112i	0.873549	+	0.486736i	$0.161813\pi$
$458$	1.16121	+	2.01127i	0.0542596	+	0.0939805i
$459$	−2.10593	−	3.64758i	−0.0982965	−	0.170254i
$460$	19.6467	−	34.0290i	0.916031	−	1.58661i
$461$	12.4955			0.581972			0.290986	−	0.956727i	$-0.406017\pi$
$461$	12.4955			0.581972			0.290986	+	0.956727i	$0.406017\pi$
$462$	0.935844	+	3.05966i	0.0435394	+	0.142348i
$463$	−0.309503			−0.0143838			−0.00719190	−	0.999974i	$-0.502289\pi$
$463$	−0.309503			−0.0143838			−0.00719190	+	0.999974i	$0.502289\pi$
$464$	−4.20233	+	7.27865i	−0.195088	+	0.337903i
$465$	3.73973	+	6.47741i	0.173426	+	0.300382i
$466$	2.71486	+	4.70227i	0.125763	+	0.217829i
$467$	−12.2387	+	21.1980i	−0.566338	+	0.980926i	0.430586	+	0.902549i	$0.358307\pi$
$467$	−12.2387	+	21.1980i	−0.566338	+	0.980926i	−0.996924	+	0.0783762i	$0.975026\pi$
$468$		0			0
$469$	−1.04668	−	3.42205i	−0.0483314	−	0.158016i
$470$	0.904302			0.0417123
$471$	−0.940659	+	1.62927i	−0.0433433	+	0.0750727i
$472$	4.72198	+	8.17871i	0.217347	+	0.376456i
$473$	4.43818	+	7.68716i	0.204068	+	0.353456i
$474$	−0.948959	+	1.64364i	−0.0435871	+	0.0754951i
$475$	−11.7120			−0.537384
$476$	−2.73106	+	2.92943i	−0.125178	+	0.134270i
$477$	−15.7152			−0.719549
$478$	2.21909	−	3.84357i	0.101499	−	0.175801i
$479$	−4.06925	−	7.04815i	−0.185929	−	0.322038i	0.757960	−	0.652301i	$-0.226196\pi$
$479$	−4.06925	−	7.04815i	−0.185929	−	0.322038i	−0.943889	+	0.330262i	$0.892863\pi$
$480$	4.48686	+	7.77147i	0.204796	+	0.354718i
$481$		0			0
$482$	4.39746			0.200299
$483$	−23.4415	−	5.40885i	−1.06662	−	0.246111i
$484$	−8.81325			−0.400602
$485$	−3.03826	+	5.26243i	−0.137960	+	0.238954i
$486$	−1.99653	−	3.45809i	−0.0905645	−	0.156862i
$487$	−2.30480	−	3.99203i	−0.104440	−	0.180896i	0.809069	−	0.587714i	$-0.199972\pi$
$487$	−2.30480	−	3.99203i	−0.104440	−	0.180896i	−0.913509	+	0.406817i	$0.866638\pi$
$488$	−4.97410	+	8.61540i	−0.225167	+	0.390001i
$489$	7.48464			0.338467
$490$	−0.336574	−	4.79630i	−0.0152049	−	0.216675i
$491$	13.0189			0.587537			0.293768	−	0.955877i	$-0.405091\pi$
$491$	13.0189			0.587537			0.293768	+	0.955877i	$0.405091\pi$
$492$	2.68591	−	4.65213i	0.121090	−	0.209734i
$493$	−0.923171	−	1.59898i	−0.0415775	−	0.0720144i
$494$		0			0
$495$	−8.55969	+	14.8258i	−0.384729	+	0.666371i
$496$	−9.12885			−0.409897
$497$	−31.7512	−	7.32624i	−1.42424	−	0.328627i
$498$	−0.328817			−0.0147347
$499$	16.1603	−	27.9905i	0.723436	−	1.25303i	−0.236178	−	0.971710i	$-0.575895\pi$
$499$	16.1603	−	27.9905i	0.723436	−	1.25303i	0.959614	−	0.281319i	$-0.0907717\pi$
$500$	8.48928	+	14.7039i	0.379652	+	0.657577i
$501$	5.45718	+	9.45211i	0.243809	+	0.422289i
$502$	−2.73900	+	4.74408i	−0.122247	+	0.211739i
$503$	−31.8253			−1.41902			−0.709509	−	0.704696i	$-0.751083\pi$
$503$	−31.8253			−1.41902			−0.709509	+	0.704696i	$0.751083\pi$
$504$	−3.21802	+	3.45176i	−0.143342	+	0.153754i
$505$	2.04256			0.0908929
$506$	−4.20838	+	7.28912i	−0.187085	+	0.324041i
$507$		0			0
$508$	1.72377	+	2.98566i	0.0764801	+	0.132467i
$509$	−1.12788	+	1.95354i	−0.0499922	+	0.0865891i	−0.889939	−	0.456080i	$-0.849253\pi$
$509$	−1.12788	+	1.95354i	−0.0499922	+	0.0865891i	0.839946	+	0.542669i	$0.182586\pi$
$510$	−0.616382			−0.0272938
$511$	0.594776	+	1.94457i	0.0263114	+	0.0860228i
$512$	−18.4807			−0.816739
$513$	20.1051	−	34.8231i	0.887663	−	1.53748i
$514$	1.84710	+	3.19927i	0.0814722	+	0.141114i
$515$	2.77461	+	4.80576i	0.122264	+	0.211767i
$516$	2.47873	−	4.29329i	0.109120	−	0.189001i
$517$	5.19512			0.228481
$518$	−1.40204	−	4.58385i	−0.0616021	−	0.201403i
$519$	−12.7236			−0.558502
$520$		0			0
$521$	−5.38562	−	9.32817i	−0.235948	−	0.408675i	0.723600	−	0.690220i	$-0.242486\pi$
$521$	−5.38562	−	9.32817i	−0.235948	−	0.408675i	−0.959548	+	0.281546i	$0.909153\pi$
$522$	−0.533934	−	0.924801i	−0.0233697	−	0.0404775i
$523$	−3.70397	+	6.41546i	−0.161963	+	0.280528i	−0.935573	−	0.353134i	$-0.885116\pi$
$523$	−3.70397	+	6.41546i	−0.161963	+	0.280528i	0.773610	+	0.633663i	$0.218449\pi$
$524$	12.3224			0.538305
$525$	−3.22232	+	3.45637i	−0.140634	+	0.150848i
$526$	−6.94909			−0.302995
$527$	1.00272	−	1.73676i	0.0436790	−	0.0756543i
$528$	8.05953	+	13.9595i	0.350746	+	0.607510i
$529$	−20.1424	−	34.8877i	−0.875757	−	1.51686i
$530$	−3.18692	+	5.51991i	−0.138431	+	0.239770i
$531$	15.1854			0.658990
$532$	−37.2567	−	8.59656i	−1.61528	−	0.372708i
$533$		0			0
$534$	−1.17424	+	2.03384i	−0.0508142	+	0.0880127i
$535$	−14.7637	−	25.5715i	−0.638290	−	1.10555i
$536$	0.712276	+	1.23370i	0.0307656	+	0.0532876i
$537$	−7.22580	+	12.5154i	−0.311816	+	0.540081i
$538$	8.06161			0.347561
$539$	−1.93358	−	27.5543i	−0.0832854	−	1.18685i
$540$	26.4983			1.14031
$541$	−16.2741	+	28.1875i	−0.699676	+	1.21188i	0.268902	+	0.963168i	$0.413339\pi$
$541$	−16.2741	+	28.1875i	−0.699676	+	1.21188i	−0.968579	+	0.248708i	$0.919994\pi$
$542$	1.93728	+	3.35546i	0.0832132	+	0.144129i
$543$	8.52445	+	14.7648i	0.365819	+	0.633617i
$544$	1.20304	−	2.08373i	0.0515799	−	0.0893391i
$545$	−20.6944			−0.886453
$546$		0			0
$547$	−13.4997			−0.577206			−0.288603	−	0.957449i	$-0.593191\pi$
$547$	−13.4997			−0.577206			−0.288603	+	0.957449i	$0.593191\pi$
$548$	9.67577	−	16.7589i	0.413329	−	0.715906i
$549$	7.99810	+	13.8531i	0.341350	+	0.591236i
$550$	0.826627	+	1.43176i	0.0352475	+	0.0610504i
$551$	8.81342	−	15.2653i	0.375464	−	0.650323i
$552$	9.57680			0.407616
$553$	11.1729	−	11.9844i	0.475119	−	0.509628i
$554$	4.10915			0.174581
$555$	−9.89284	+	17.1349i	−0.419928	+	0.727336i
$556$	−5.34623	−	9.25994i	−0.226731	−	0.392709i
$557$	14.8851	+	25.7818i	0.630703	+	1.09241i	0.987408	+	0.158193i	$0.0505668\pi$
$557$	14.8851	+	25.7818i	0.630703	+	1.09241i	−0.356705	+	0.934217i	$0.616100\pi$
$558$	0.579941	−	1.00449i	0.0245509	−	0.0425233i
$559$		0			0
$560$	−7.08483	−	23.1632i	−0.299389	−	0.978826i
$561$	−3.54105			−0.149503
$562$	0.709566	−	1.22900i	0.0299312	−	0.0518424i
$563$	−7.06629	−	12.2392i	−0.297809	−	0.515819i	0.677826	−	0.735223i	$-0.262922\pi$
$563$	−7.06629	−	12.2392i	−0.297809	−	0.515819i	−0.975634	+	0.219403i	$0.929589\pi$
$564$	−1.45074	−	2.51275i	−0.0610872	−	0.105806i
$565$	10.3000	−	17.8401i	0.433324	−	0.750538i
$566$	8.25410			0.346946
$567$	−0.813601	−	2.66000i	−0.0341680	−	0.111710i
$568$	12.9717			0.544280
$569$	12.1270	−	21.0046i	0.508391	−	0.880558i	−0.491562	−	0.870842i	$-0.663574\pi$
$569$	12.1270	−	21.0046i	0.508391	−	0.880558i	0.999953	−	0.00971585i	$-0.00309270\pi$
$570$	−2.94227	−	5.09616i	−0.123238	−	0.213455i
$571$	−0.604159	−	1.04643i	−0.0252832	−	0.0437919i	0.853107	−	0.521736i	$-0.174715\pi$
$571$	−0.604159	−	1.04643i	−0.0252832	−	0.0437919i	−0.878390	+	0.477944i	$0.841382\pi$
$572$		0			0
$573$	16.1514			0.674732
$574$	1.17910	−	1.26475i	0.0492149	−	0.0527895i
$575$	−12.4307			−0.518394
$576$	−5.35657	+	9.27786i	−0.223191	+	0.386577i
$577$	7.30518	+	12.6529i	0.304119	+	0.526749i	0.977065	−	0.212943i	$-0.0683047\pi$
$577$	7.30518	+	12.6529i	0.304119	+	0.526749i	−0.672946	+	0.739692i	$0.734971\pi$
$578$	−2.19643	−	3.80433i	−0.0913595	−	0.158239i
$579$	2.22575	−	3.85510i	0.0924988	−	0.160213i
$580$	11.6160			0.482328
$581$	2.76600	+	0.638224i	0.114753	+	0.0264780i
$582$	−0.726951			−0.0301331
$583$	−18.3085	+	31.7113i	−0.758262	+	1.31335i
$584$	−0.404749	−	0.701046i	−0.0167486	−	0.0290095i
$585$		0			0
$586$	−2.34841	+	4.06757i	−0.0970120	+	0.168030i
$587$	21.5095			0.887793			0.443897	−	0.896078i	$-0.353596\pi$
$587$	21.5095			0.887793			0.443897	+	0.896078i	$0.353596\pi$
$588$	−12.7874	+	8.62977i	−0.527343	+	0.355886i
$589$	19.1457			0.788884
$590$	3.07949	−	5.33383i	0.126780	−	0.219590i
$591$	−6.69168	−	11.5903i	−0.275259	−	0.476763i
$592$	−12.0744	−	20.9135i	−0.496256	−	0.859541i
$593$	1.32429	−	2.29373i	0.0543820	−	0.0941923i	−0.837553	−	0.546356i	$-0.816014\pi$
$593$	1.32429	−	2.29373i	0.0543820	−	0.0941923i	0.891935	+	0.452164i	$0.149348\pi$
$594$	−5.67602			−0.232890
$595$	5.18499	+	1.19638i	0.212564	+	0.0490467i
$596$	−35.6027			−1.45834
$597$	1.99846	−	3.46143i	0.0817915	−	0.141667i
$598$		0			0
$599$	20.1250	+	34.8576i	0.822287	+	1.42424i	0.903975	+	0.427584i	$0.140635\pi$
$599$	20.1250	+	34.8576i	0.822287	+	1.42424i	−0.0816889	+	0.996658i	$0.526031\pi$
$600$	0.940558	−	1.62909i	0.0383981	−	0.0665075i
$601$	38.3449			1.56412			0.782061	−	0.623202i	$-0.214169\pi$
$601$	38.3449			1.56412			0.782061	+	0.623202i	$0.214169\pi$
$602$	1.08816	−	1.16719i	0.0443499	−	0.0475712i
$603$	2.29060			0.0932806
$604$	1.54958	−	2.68395i	0.0630515	−	0.109208i
$605$	5.85480	+	10.1408i	0.238031	+	0.412283i
$606$	0.122179	+	0.211620i	0.00496317	+	0.00859646i
$607$	−21.2773	+	36.8534i	−0.863620	+	1.49583i	0.00479063	+	0.999989i	$0.498475\pi$
$607$	−21.2773	+	36.8534i	−0.863620	+	1.49583i	−0.868411	+	0.495845i	$0.834858\pi$
$608$	22.9706			0.931582
$609$	−2.08015	−	6.80089i	−0.0842921	−	0.275586i
$610$	6.48782			0.262684
$611$		0			0
$612$	−1.28180	−	2.22014i	−0.0518136	−	0.0897438i
$613$	−7.63261	−	13.2201i	−0.308278	−	0.533953i	0.669708	−	0.742625i	$-0.266419\pi$
$613$	−7.63261	−	13.2201i	−0.308278	−	0.533953i	−0.977986	+	0.208672i	$0.933086\pi$
$614$	−1.15773	+	2.00524i	−0.0467221	+	0.0809251i
$615$	−7.13718			−0.287799
$616$	3.21616	+	10.5150i	0.129583	+	0.423660i
$617$	13.9812			0.562863			0.281431	−	0.959581i	$-0.409191\pi$
$617$	13.9812			0.562863			0.281431	+	0.959581i	$0.409191\pi$
$618$	−0.331934	+	0.574926i	−0.0133523	+	0.0231269i
$619$	4.25792	+	7.37494i	0.171140	+	0.296424i	0.938819	−	0.344411i	$-0.111921\pi$
$619$	4.25792	+	7.37494i	0.171140	+	0.296424i	−0.767678	+	0.640835i	$0.778588\pi$
$620$	6.30845	+	10.9265i	0.253353	+	0.438821i
$621$	21.3388	−	36.9598i	0.856295	−	1.48315i
$622$	4.40331			0.176557
$623$	13.8253	−	14.8294i	0.553897	−	0.594129i
$624$		0			0
$625$	15.1856	−	26.3023i	0.607425	−	1.05209i
$626$	1.34682	+	2.33275i	0.0538296	+	0.0932356i
$627$	−16.9030	−	29.2769i	−0.675042	−	1.16921i
$628$	−1.58677	+	2.74837i	−0.0633190	+	0.109672i
$629$	5.30504			0.211526
$630$	2.99884	+	0.691949i	0.119477	+	0.0275679i
$631$	36.8292			1.46615			0.733074	−	0.680149i	$-0.238085\pi$
$631$	36.8292			1.46615			0.733074	+	0.680149i	$0.238085\pi$
$632$	−3.26123	+	5.64861i	−0.129725	+	0.224690i
$633$	10.8615	+	18.8127i	0.431707	+	0.747739i
$634$	1.36006	+	2.35570i	0.0540150	+	0.0935567i
$635$	2.29027	−	3.96686i	0.0908865	−	0.157420i
$636$	20.4507			0.810922
$637$		0			0
$638$	−2.48818			−0.0985081
$639$	10.4289	−	18.0634i	0.412561	−	0.714576i
$640$	10.0235	+	17.3612i	0.396214	+	0.686263i
$641$	−12.9374	−	22.4082i	−0.510996	−	0.885070i	−0.999919	−	0.0127435i	$-0.995944\pi$
$641$	−12.9374	−	22.4082i	−0.510996	−	0.885070i	0.488923	−	0.872327i	$-0.337390\pi$
$642$	1.76622	−	3.05918i	0.0697071	−	0.120736i
$643$	40.5252			1.59816			0.799078	−	0.601227i	$-0.205321\pi$
$643$	40.5252			1.59816			0.799078	+	0.601227i	$0.205321\pi$
$644$	−39.5427	−	9.12404i	−1.55820	−	0.359538i
$645$	−6.58666			−0.259350
$646$	−0.788896	+	1.36641i	−0.0310387	+	0.0537606i
$647$	−0.892002	−	1.54499i	−0.0350682	−	0.0607399i	0.847959	−	0.530062i	$-0.177832\pi$
$647$	−0.892002	−	1.54499i	−0.0350682	−	0.0607399i	−0.883027	+	0.469322i	$0.844498\pi$
$648$	0.553661	+	0.958969i	0.0217499	+	0.0376719i
$649$	17.6913	−	30.6423i	0.694445	−	1.20281i
$650$		0			0
$651$	5.26754	−	5.65014i	0.206451	−	0.221446i
$652$	12.6256			0.494457
$653$	−6.20210	+	10.7424i	−0.242707	+	0.420381i	−0.961484	−	0.274860i	$-0.911369\pi$
$653$	−6.20210	+	10.7424i	−0.242707	+	0.420381i	0.718778	+	0.695240i	$0.244702\pi$
$654$	−1.23787	−	2.14405i	−0.0484044	−	0.0838389i
$655$	−8.18597	−	14.1785i	−0.319852	−	0.554000i
$656$	4.35554	−	7.54402i	0.170055	−	0.294545i
$657$	−1.30163			−0.0507815
$658$	−0.273171	−	0.893110i	−0.0106493	−	0.0348171i
$659$	−1.12867			−0.0439668			−0.0219834	−	0.999758i	$-0.506998\pi$
$659$	−1.12867			−0.0439668			−0.0219834	+	0.999758i	$0.506998\pi$
$660$	11.1390	−	19.2933i	0.433585	−	0.750991i
$661$	14.4627	+	25.0502i	0.562534	+	0.974338i	0.997274	+	0.0737821i	$0.0235069\pi$
$661$	14.4627	+	25.0502i	0.562534	+	0.974338i	−0.434740	+	0.900556i	$0.643160\pi$
$662$	0.310913	+	0.538517i	0.0120840	+	0.0209301i
$663$		0			0
$664$	−1.13003			−0.0438535
$665$	14.8588	+	48.5796i	0.576200	+	1.88384i
$666$	3.06828			0.118893
$667$	9.35421	−	16.2020i	0.362196	−	0.627342i
$668$	9.20556	+	15.9445i	0.356174	+	0.616911i
$669$	−6.83874	−	11.8451i	−0.264401	−	0.457956i
$670$	0.464518	−	0.804568i	0.0179459	−	0.0310832i
$671$	37.2718			1.43886
$672$	6.31990	−	6.77893i	0.243795	−	0.261503i
$673$	−7.09960			−0.273669			−0.136835	−	0.990594i	$-0.543693\pi$
$673$	−7.09960			−0.273669			−0.136835	+	0.990594i	$0.543693\pi$
$674$	−2.14498	+	3.71521i	−0.0826214	+	0.143104i
$675$	−4.19145	−	7.25980i	−0.161329	−	0.279430i
$676$		0			0
$677$	25.2010	−	43.6494i	0.968552	−	1.67758i	0.268800	−	0.963196i	$-0.413373\pi$
$677$	25.2010	−	43.6494i	0.968552	−	1.67758i	0.699752	−	0.714386i	$-0.253294\pi$
$678$	2.46443			0.0946458
$679$	6.11509	+	1.41099i	0.234676	+	0.0541488i
$680$	−2.11828			−0.0812324
$681$	8.79213	−	15.2284i	0.336915	−	0.583554i
$682$	−1.35129	−	2.34050i	−0.0517435	−	0.0896224i
$683$	−13.7641	−	23.8401i	−0.526669	−	0.912217i	−0.999517	−	0.0310735i	$-0.990107\pi$
$683$	−13.7641	−	23.8401i	−0.526669	−	0.912217i	0.472848	−	0.881144i	$-0.343226\pi$
$684$	12.2372	−	21.1954i	0.467901	−	0.810428i
$685$	−25.7112			−0.982373
$686$	−4.63527	+	1.78127i	−0.176975	+	0.0680093i
$687$	−9.90037			−0.377723
$688$	4.01958	−	6.96212i	0.153245	−	0.265428i
$689$		0			0
$690$	−3.12280	−	5.40885i	−0.118883	−	0.205912i
$691$	12.1669	−	21.0737i	0.462851	−	0.801682i	−0.536251	−	0.844059i	$-0.680160\pi$
$691$	12.1669	−	21.0737i	0.462851	−	0.801682i	0.999102	+	0.0423772i	$0.0134931\pi$
$692$	−21.4630			−0.815901
$693$	17.2280	+	3.97517i	0.654439	+	0.151004i
$694$	6.11884			0.232268
$695$	−7.10319	+	12.3031i	−0.269439	+	0.466683i
$696$	1.41556	+	2.45182i	0.0536566	+	0.0929360i
$697$	0.956829	+	1.65728i	0.0362425	+	0.0627738i
$698$	−3.04352	+	5.27153i	−0.115199	+	0.199531i
$699$	−23.1467			−0.875488
$700$	−5.43565	+	5.83045i	−0.205448	+	0.220370i
$701$	−20.5588			−0.776495			−0.388248	−	0.921555i	$-0.626919\pi$
$701$	−20.5588			−0.776495			−0.388248	+	0.921555i	$0.626919\pi$
$702$		0			0
$703$	25.3234	+	43.8613i	0.955088	+	1.65426i
$704$	12.4811	+	21.6178i	0.470397	+	0.814752i
$705$	−1.92751	+	3.33854i	−0.0725940	+	0.125737i
$706$	7.31027			0.275126
$707$	−0.617017	−	2.01728i	−0.0232053	−	0.0758678i
$708$	−19.7612			−0.742673
$709$	−20.4544	+	35.4281i	−0.768183	+	1.33053i	0.170364	+	0.985381i	$0.445506\pi$
$709$	−20.4544	+	35.4281i	−0.768183	+	1.33053i	−0.938547	+	0.345151i	$0.887828\pi$
$710$	−4.22981	−	7.32624i	−0.158742	−	0.274949i
$711$	5.24388	+	9.08267i	0.196661	+	0.340627i
$712$	−4.03543	+	6.98956i	−0.151234	+	0.261945i
$713$	20.3204			0.761006
$714$	0.186196	+	0.608753i	0.00696822	+	0.0227820i
$715$		0			0
$716$	−12.1890	+	21.1119i	−0.455524	+	0.788990i
$717$	9.45989	+	16.3850i	0.353286	+	0.611910i
$718$	−1.93401	−	3.34981i	−0.0721767	−	0.125014i
$719$	0.599734	−	1.03877i	0.0223663	−	0.0387396i	−0.854626	−	0.519245i	$-0.826213\pi$
$719$	0.599734	−	1.03877i	0.0223663	−	0.0387396i	0.876992	+	0.480505i	$0.159547\pi$
$720$	15.5047			0.577826
$721$	3.90813	−	4.19199i	0.145546	−	0.156118i
$722$	−9.96865			−0.370995
$723$	−9.37311	+	16.2347i	−0.348590	+	0.603775i
$724$	14.3796	+	24.9063i	0.534415	+	0.925634i
$725$	−1.83739	−	3.18246i	−0.0682390	−	0.118193i
$726$	−0.700425	+	1.21317i	−0.0259952	+	0.0450250i
$727$	−2.06230			−0.0764865			−0.0382433	−	0.999268i	$-0.512176\pi$
$727$	−2.06230			−0.0764865			−0.0382433	+	0.999268i	$0.512176\pi$
$728$		0			0
$729$	20.1764			0.747273
$730$	−0.263961	+	0.457194i	−0.00976964	+	0.0169215i
$731$	0.883025	+	1.52944i	0.0326599	+	0.0565685i
$732$	−10.4082	−	18.0275i	−0.384697	−	0.666315i
$733$	−15.0310	+	26.0345i	−0.555184	+	0.961606i	0.442706	+	0.896667i	$0.354019\pi$
$733$	−15.0310	+	26.0345i	−0.555184	+	0.961606i	−0.997889	+	0.0649392i	$0.979315\pi$
$734$	3.05441			0.112740
$735$	18.4246	+	8.98066i	0.679601	+	0.331257i
$736$	24.3801			0.898662
$737$	2.66861	−	4.62216i	0.0982993	−	0.170259i
$738$	0.553401	+	0.958519i	0.0203710	+	0.0352836i
$739$	−22.1274	−	38.3257i	−0.813969	−	1.40984i	−0.910066	−	0.414464i	$-0.863969\pi$
$739$	−22.1274	−	38.3257i	−0.813969	−	1.40984i	0.0960970	−	0.995372i	$-0.469364\pi$
$740$	−16.6880	+	28.9044i	−0.613461	+	1.06255i
$741$		0			0
$742$	6.41430	+	1.48003i	0.235476	+	0.0543335i
$743$	−8.62651			−0.316476			−0.158238	−	0.987401i	$-0.550581\pi$
$743$	−8.62651			−0.316476			−0.158238	+	0.987401i	$0.550581\pi$
$744$	−1.53753	+	2.66308i	−0.0563686	+	0.0976334i
$745$	23.6515	+	40.9656i	0.866524	+	1.50086i
$746$	−4.15097	−	7.18969i	−0.151978	−	0.263233i
$747$	−0.908511	+	1.57359i	−0.0332407	+	0.0575746i
$748$	−5.97329			−0.218405
$749$	−20.7952	+	22.3056i	−0.759839	+	0.815028i
$750$	2.69871			0.0985430
$751$	−2.86105	+	4.95549i	−0.104401	+	0.180828i	−0.913493	−	0.406853i	$-0.866626\pi$
$751$	−2.86105	+	4.95549i	−0.104401	+	0.180828i	0.809092	+	0.587682i	$0.199959\pi$
$752$	−2.35256	−	4.07476i	−0.0857891	−	0.148591i
$753$	−11.6763	−	20.2239i	−0.425506	−	0.736998i
$754$		0			0
$755$	−4.11765			−0.149857
$756$	−8.00460	−	26.1704i	−0.291125	−	0.951807i
$757$	−34.7222			−1.26200			−0.631000	−	0.775783i	$-0.717355\pi$
$757$	−34.7222			−1.26200			−0.631000	+	0.775783i	$0.717355\pi$
$758$	1.41927	−	2.45824i	0.0515501	−	0.0892873i
$759$	−17.9402	−	31.0733i	−0.651187	−	1.12789i
$760$	−10.1115	−	17.5137i	−0.366783	−	0.635287i
$761$	26.5867	−	46.0496i	0.963768	−	1.66930i	0.250880	−	0.968018i	$-0.419280\pi$
$761$	26.5867	−	46.0496i	0.963768	−	1.66930i	0.712888	−	0.701278i	$-0.247387\pi$
$762$	0.547981			0.0198513
$763$	6.25137	+	20.4383i	0.226315	+	0.739917i
$764$	27.2452			0.985699
$765$	−1.70304	+	2.94976i	−0.0615736	+	0.106649i
$766$	4.12265	+	7.14063i	0.148957	+	0.258002i
$767$		0			0
$768$	6.03145	−	10.4468i	0.217641	−	0.376966i
$769$	4.91157			0.177116			0.0885578	−	0.996071i	$-0.471774\pi$
$769$	4.91157			0.177116			0.0885578	+	0.996071i	$0.471774\pi$
$770$	4.88999	−	5.24516i	0.176223	−	0.189022i
$771$	−15.7483			−0.567160
$772$	3.75455	−	6.50306i	0.135129	−	0.234050i
$773$	11.4903	+	19.9018i	0.413279	+	0.715819i	0.995246	−	0.0973926i	$-0.0310502\pi$
$773$	11.4903	+	19.9018i	0.413279	+	0.715819i	−0.581967	+	0.813212i	$0.697717\pi$
$774$	0.510715	+	0.884585i	0.0183573	+	0.0317957i
$775$	1.99571	−	3.45667i	0.0716881	−	0.124167i
$776$	−2.49827			−0.0896826
$777$	19.9113	+	4.59430i	0.714313	+	0.164820i
$778$	4.39178			0.157453
$779$	−9.13476	+	15.8219i	−0.327287	+	0.566877i
$780$		0			0
$781$	−24.2998	−	42.0885i	−0.869515	−	1.50604i
$782$	−0.837302	+	1.45025i	−0.0299419	+	0.0518608i
$783$	12.6164			0.450874
$784$	−20.7364	+	13.9943i	−0.740585	+	0.499796i
$785$	4.21648			0.150493
$786$	0.979309	−	1.69621i	0.0349308	−	0.0605019i
$787$	1.59387	+	2.76067i	0.0568154	+	0.0984071i	0.893034	−	0.449989i	$-0.148572\pi$
$787$	1.59387	+	2.76067i	0.0568154	+	0.0984071i	−0.836219	+	0.548396i	$0.815239\pi$
$788$	−11.2880	−	19.5514i	−0.402119	−	0.696490i
$789$	14.8119	−	25.6549i	0.527316	−	0.913339i
$790$	4.25368			0.151339
$791$	−20.7307	−	4.78338i	−0.737099	−	0.170077i
$792$	−7.03836			−0.250097
$793$		0			0
$794$	−2.12927	−	3.68800i	−0.0755650	−	0.130882i
$795$	−13.5857	−	23.5312i	−0.481837	−	0.834566i
$796$	3.37114	−	5.83899i	0.119487	−	0.206958i
$797$	54.6509			1.93584			0.967918	−	0.251267i	$-0.0808472\pi$
$797$	54.6509			1.93584			0.967918	+	0.251267i	$0.0808472\pi$
$798$	−4.14429	+	4.44530i	−0.146706	+	0.157362i
$799$	1.03363			0.0365670
$800$	2.39442	−	4.14725i	0.0846554	−	0.146628i
$801$	6.48875	+	11.2388i	0.229269	+	0.397105i
$802$	0.889604	+	1.54084i	0.0314130	+	0.0544089i
$803$	−1.51643	+	2.62653i	−0.0535136	+	0.0926883i
$804$	−2.98084			−0.105126
$805$	15.7705	+	51.5604i	0.555838	+	1.81727i
$806$		0			0
$807$	−17.1832	+	29.7622i	−0.604877	+	1.04768i
$808$	0.419884	+	0.727260i	0.0147715	+	0.0255849i
$809$	10.1498	+	17.5799i	0.356847	+	0.618077i	0.987432	−	0.158043i	$-0.0505185\pi$
$809$	10.1498	+	17.5799i	0.356847	+	0.618077i	−0.630585	+	0.776120i	$0.717185\pi$
$810$	0.361076	−	0.625401i	0.0126869	−	0.0219744i
$811$	2.43587			0.0855350			0.0427675	−	0.999085i	$-0.486383\pi$
$811$	2.43587			0.0855350			0.0427675	+	0.999085i	$0.486383\pi$
$812$	−3.50895	−	11.4722i	−0.123140	−	0.402596i
$813$	−16.5171			−0.579280
$814$	3.57461	−	6.19141i	0.125290	−	0.217009i
$815$	−8.38742	−	14.5274i	−0.293799	−	0.508874i
$816$	1.60353	+	2.77740i	0.0561348	+	0.0972284i
$817$	−8.43015	+	14.6015i	−0.294934	+	0.510840i
$818$	−1.57452			−0.0550519
$819$		0			0
$820$	−12.0395			−0.420438
$821$	−22.6762	+	39.2763i	−0.791405	+	1.37075i	0.133692	+	0.991023i	$0.457317\pi$
$821$	−22.6762	+	39.2763i	−0.791405	+	1.37075i	−0.925097	+	0.379731i	$0.876017\pi$
$822$	−1.53795	−	2.66380i	−0.0536421	−	0.0929108i
$823$	1.37871	+	2.38800i	0.0480588	+	0.0832403i	0.889054	−	0.457802i	$-0.151363\pi$
$823$	1.37871	+	2.38800i	0.0480588	+	0.0832403i	−0.840995	+	0.541042i	$0.818030\pi$
$824$	−1.14074	+	1.97581i	−0.0397394	+	0.0688307i
$825$	−7.04776			−0.245372
$826$	−6.19806	−	1.43013i	−0.215658	−	0.0497607i
$827$	−8.64504			−0.300618			−0.150309	−	0.988639i	$-0.548027\pi$
$827$	−8.64504			−0.300618			−0.150309	+	0.988639i	$0.548027\pi$
$828$	12.9881	−	22.4960i	0.451366	−	0.781789i
$829$	14.7871	+	25.6119i	0.513576	+	0.889540i	0.999876	+	0.0157478i	$0.00501289\pi$
$829$	14.7871	+	25.6119i	0.513576	+	0.889540i	−0.486300	+	0.873792i	$0.661654\pi$
$830$	0.368479	+	0.638224i	0.0127901	+	0.0221531i
$831$	−8.75858	+	15.1703i	−0.303832	+	0.526252i
$832$		0			0
$833$	−0.384708	−	5.48222i	−0.0133293	−	0.189948i
$834$	−1.69955			−0.0588505
$835$	12.2308	−	21.1844i	0.423266	−	0.733117i
$836$	−28.5132	−	49.3863i	−0.986150	−	1.70806i
$837$	6.85177	+	11.8676i	0.236832	+	0.410204i
$838$	−4.04096	+	6.99914i	−0.139593	+	0.241781i
$839$	25.2473			0.871633			0.435817	−	0.900035i	$-0.356460\pi$
$839$	25.2473			0.871633			0.435817	+	0.900035i	$0.356460\pi$
$840$	−7.95049	−	1.83449i	−0.274318	−	0.0632958i
$841$	−23.4694			−0.809289
$842$	5.37028	−	9.30159i	0.185072	−	0.320554i
$843$	3.02485	+	5.23920i	0.104182	+	0.180448i
$844$	18.3220	+	31.7346i	0.630669	+	1.09235i
$845$		0			0
$846$	0.597818			0.0205534
$847$	8.24669	−	8.84567i	0.283360	−	0.303941i
$848$	33.1634			1.13884
$849$	−17.5935	+	30.4728i	−0.603807	+	1.04582i
$850$	0.164466	+	0.284864i	0.00564115	+	0.00977076i
$851$	26.8772	+	46.5526i	0.921338	+	1.59580i
$852$	−13.5715	+	23.5064i	−0.464950	+	0.805318i
$853$	−35.1368			−1.20306			−0.601531	−	0.798850i	$-0.705442\pi$
$853$	−35.1368			−1.20306			−0.601531	+	0.798850i	$0.705442\pi$
$854$	−1.95984	−	6.40752i	−0.0670643	−	0.219261i
$855$	−32.5176			−1.11208
$856$	6.06986	−	10.5133i	0.207463	−	0.359337i
$857$	0.671345	+	1.16280i	0.0229327	+	0.0397206i	0.877264	−	0.480008i	$-0.159366\pi$
$857$	0.671345	+	1.16280i	0.0229327	+	0.0397206i	−0.854331	+	0.519729i	$0.826033\pi$
$858$		0			0
$859$	−2.38386	+	4.12897i	−0.0813363	+	0.140879i	−0.903824	−	0.427904i	$-0.859252\pi$
$859$	−2.38386	+	4.12897i	−0.0813363	+	0.140879i	0.822488	+	0.568783i	$0.192585\pi$
$860$	−11.1108			−0.378877
$861$	2.15600	+	7.04885i	0.0734762	+	0.240224i
$862$	1.04994			0.0357612
$863$	13.3052	−	23.0453i	0.452915	−	0.784472i	−0.545650	−	0.838013i	$-0.683717\pi$
$863$	13.3052	−	23.0453i	0.452915	−	0.784472i	0.998566	+	0.0535407i	$0.0170507\pi$
$864$	8.22062	+	14.2385i	0.279671	+	0.484405i
$865$	14.2583	+	24.6960i	0.484795	+	0.839690i
$866$	−5.46875	+	9.47216i	−0.185836	+	0.321877i
$867$	18.7266			0.635989
$868$	8.88566	−	9.53106i	0.301599	−	0.323505i
$869$	24.4370			0.828967
$870$	0.923171	−	1.59898i	0.0312984	−	0.0542105i
$871$		0			0
$872$	−4.25410	−	7.36831i	−0.144062	−	0.249523i
$873$	−2.00854	+	3.47890i	−0.0679788	+	0.117743i
$874$	−15.9873			−0.540778
$875$	−22.7015	−	5.23812i	−0.767451	−	0.177081i
$876$	1.69385			0.0572300
$877$	−4.01848	+	6.96022i	−0.135695	+	0.235030i	−0.925863	−	0.377860i	$-0.876660\pi$
$877$	−4.01848	+	6.96022i	−0.135695	+	0.235030i	0.790168	+	0.612890i	$0.209993\pi$
$878$	−3.42694	−	5.93564i	−0.115654	−	0.200318i
$879$	−10.0112	−	17.3399i	−0.337670	−	0.584861i
$880$	18.0633	−	31.2866i	0.608915	−	1.05467i
$881$	−54.6697			−1.84187			−0.920935	−	0.389716i	$-0.872573\pi$
$881$	−54.6697			−1.84187			−0.920935	+	0.389716i	$0.872573\pi$
$882$	−0.222503	−	3.17075i	−0.00749208	−	0.106765i
$883$	−8.45085			−0.284394			−0.142197	−	0.989838i	$-0.545417\pi$
$883$	−8.45085			−0.284394			−0.142197	+	0.989838i	$0.545417\pi$
$884$		0			0
$885$	13.1277	+	22.7379i	0.441284	+	0.764327i
$886$	−3.68088	−	6.37547i	−0.123662	−	0.214188i
$887$	5.17784	−	8.96829i	0.173855	−	0.301126i	−0.765909	−	0.642948i	$-0.777711\pi$
$887$	5.17784	−	8.96829i	0.173855	−	0.301126i	0.939764	+	0.341823i	$0.111044\pi$
$888$	−8.13457			−0.272978
$889$	−4.60961	−	1.06361i	−0.154601	−	0.0356725i
$890$	5.26349			0.176432
$891$	2.07434	−	3.59286i	0.0694930	−	0.120365i
$892$	−11.5361	−	19.9811i	−0.386256	−	0.669016i
$893$	4.93396	+	8.54587i	0.165109	+	0.285977i
$894$	−2.82949	+	4.90082i	−0.0946323	+	0.163908i
$895$	32.3895			1.08266
$896$	14.1185	−	15.1439i	0.471665	−	0.505923i
$897$		0			0
$898$	−1.98461	+	3.43745i	−0.0662274	+	0.114709i
$899$	3.00359	+	5.20237i	0.100175	+	0.173509i
$900$	−2.55117	−	4.41875i	−0.0850389	−	0.147292i
$901$	−3.64268	+	6.30931i	−0.121355	+	0.210194i
$902$	2.57890			0.0858680
$903$	1.98970	+	6.50514i	0.0662129	+	0.216478i
$904$	8.46935			0.281686
$905$	19.1053	−	33.0914i	0.635082	−	1.09999i
$906$	−0.246303	−	0.426609i	−0.00818287	−	0.0141731i
$907$	−9.24019	−	16.0045i	−0.306815	−	0.531420i	0.670849	−	0.741594i	$-0.265930\pi$
$907$	−9.24019	−	16.0045i	−0.306815	−	0.531420i	−0.977664	+	0.210175i	$0.932597\pi$
$908$	14.8312	−	25.6884i	0.492190	−	0.852498i
$909$	1.35030			0.0447867
$910$		0			0
$911$	−26.6282			−0.882230			−0.441115	−	0.897451i	$-0.645417\pi$
$911$	−26.6282			−0.882230			−0.441115	+	0.897451i	$0.645417\pi$
$912$	−15.3088	+	26.5155i	−0.506924	+	0.878017i
$913$	2.11687	+	3.66653i	0.0700582	+	0.121344i
$914$	−0.0874022	−	0.151385i	−0.00289101	−	0.00500737i
$915$	−13.8287	+	23.9520i	−0.457162	+	0.791828i
$916$	−16.7007			−0.551805
$917$	−11.5302	+	12.3677i	−0.380761	+	0.408417i
$918$	−1.12931			−0.0372727
$919$	5.57467	−	9.65561i	0.183891	−	0.318509i	−0.759311	−	0.650728i	$-0.774464\pi$
$919$	5.57467	−	9.65561i	0.183891	−	0.318509i	0.943202	+	0.332219i	$0.107797\pi$
$920$	−10.7319	−	18.5883i	−0.353822	−	0.612837i
$921$	−4.93536	−	8.54829i	−0.162626	−	0.281676i
$922$	1.67518	−	2.90149i	0.0551690	−	0.0955555i
$923$		0			0
$924$	−22.4194	−	5.17302i	−0.737544	−	0.170180i
$925$	10.5587			0.347166
$926$	−0.0414927	+	0.0718675i	−0.00136354	+	0.00236171i
$927$	1.83424	+	3.17700i	0.0602445	+	0.104347i
$928$	3.60365	+	6.24170i	0.118296	+	0.204894i
$929$	−3.87255	+	6.70745i	−0.127054	+	0.220064i	−0.922534	−	0.385916i	$-0.873886\pi$
$929$	−3.87255	+	6.70745i	−0.127054	+	0.220064i	0.795480	+	0.605980i	$0.207219\pi$
$930$	2.00543			0.0657607
$931$	43.4898	−	29.3498i	1.42532	−	0.961901i
$932$	−39.0455			−1.27898
$933$	−9.38559	+	16.2563i	−0.307270	+	0.532208i
$934$	3.28149	+	5.68371i	0.107374	+	0.185977i
$935$	3.96817	+	6.87306i	0.129773	+	0.224773i
$936$		0			0
$937$	36.4239			1.18992			0.594959	−	0.803756i	$-0.297168\pi$
$937$	36.4239			1.18992			0.594959	+	0.803756i	$0.297168\pi$
$938$	−0.934932	−	0.215725i	−0.0305266	−	0.00704367i
$939$	−11.4829			−0.374729
$940$	−3.25145	+	5.63168i	−0.106051	+	0.183685i
$941$	9.89466	+	17.1381i	0.322557	+	0.558685i	0.981015	−	0.193933i	$-0.0621243\pi$
$941$	9.89466	+	17.1381i	0.322557	+	0.558685i	−0.658458	+	0.752617i	$0.728791\pi$
$942$	0.252214	+	0.436848i	0.00821759	+	0.0142333i
$943$	−9.69526	+	16.7927i	−0.315721	+	0.546845i
$944$	−32.0454			−1.04299
$945$	−24.7949	+	26.5958i	−0.806577	+	0.865161i
$946$	2.37998			0.0773798
$947$	−4.97398	+	8.61519i	−0.161633	+	0.279956i	−0.935454	−	0.353448i	$-0.885009\pi$
$947$	−4.97398	+	8.61519i	−0.161633	+	0.279956i	0.773822	+	0.633403i	$0.218343\pi$
$948$	−6.82403	−	11.8196i	−0.221634	−	0.383882i
$949$		0			0
$950$	−1.57014	+	2.71957i	−0.0509422	+	0.0882345i
$951$	−11.5958			−0.376020
$952$	0.639889	+	2.09206i	0.0207389	+	0.0678042i
$953$	0.0211134			0.000683929			0.000341965	−	1.00000i	$-0.499891\pi$
$953$	0.0211134			0.000683929			0.000341965		1.00000i	$0.499891\pi$
$954$	−2.10682	+	3.64912i	−0.0682108	+	0.118144i
$955$	−18.0995	−	31.3493i	−0.585686	−	1.01444i
$956$	15.9576	+	27.6394i	0.516106	+	0.893922i
$957$	5.30352	−	9.18596i	0.171438	−	0.296940i
$958$	−2.18214			−0.0705017
$959$	7.76681	+	25.3929i	0.250804	+	0.819981i
$960$	−18.5230			−0.597827
$961$	12.2376	−	21.1962i	0.394761	−	0.683747i
$962$		0			0
$963$	−9.76001	−	16.9048i	−0.314512	−	0.544751i
$964$	−15.8112	+	27.3858i	−0.509245	+	0.882039i
$965$	−9.97685			−0.321166
$966$	−4.39858	+	4.71806i	−0.141522	+	0.151801i
$967$	−19.8102			−0.637053			−0.318526	−	0.947914i	$-0.603188\pi$
$967$	−19.8102			−0.637053			−0.318526	+	0.947914i	$0.603188\pi$
$968$	−2.40711	+	4.16923i	−0.0773674	+	0.134004i
$969$	−3.36304	−	5.82495i	−0.108036	−	0.187124i
$970$	0.814635	+	1.41099i	0.0261563	+	0.0453041i
$971$	1.80887	−	3.13305i	0.0580493	−	0.100544i	−0.835540	−	0.549429i	$-0.814845\pi$
$971$	1.80887	−	3.13305i	0.0580493	−	0.100544i	0.893590	+	0.448885i	$0.148179\pi$
$972$	28.7144			0.921015
$973$	14.2966	+	3.29877i	0.458326	+	0.105754i
$974$	−1.23595			−0.0396024
$975$		0			0
$976$	−16.8782	−	29.2339i	−0.540258	−	0.935755i
$977$	−1.08085	−	1.87208i	−0.0345793	−	0.0598931i	0.848218	−	0.529648i	$-0.177676\pi$
$977$	−1.08085	−	1.87208i	−0.0345793	−	0.0598931i	−0.882797	+	0.469754i	$0.844342\pi$
$978$	1.00341	−	1.73796i	0.0320855	−	0.0555737i
$979$	30.2382			0.966416
$980$	31.0799	+	15.1492i	0.992810	+	0.483924i
$981$	−13.6807			−0.436792
$982$	1.74535	−	3.02304i	0.0556965	−	0.0964692i
$983$	15.0545	+	26.0752i	0.480165	+	0.831671i	0.999741	−	0.0227535i	$-0.00724329\pi$
$983$	15.0545	+	26.0752i	0.480165	+	0.831671i	−0.519576	+	0.854424i	$0.673910\pi$
$984$	−1.46717	−	2.54121i	−0.0467717	−	0.0810109i
$985$	−14.9977	+	25.9767i	−0.477865	+	0.827687i
$986$	−0.495051			−0.0157656
$987$	3.87948	+	0.895146i	0.123485	+	0.0284928i
$988$		0			0
$989$	−8.94742	+	15.4974i	−0.284511	+	0.492788i
$990$	2.29507	+	3.97517i	0.0729420	+	0.126339i
$991$	13.5730	+	23.5092i	0.431161	+	0.746793i	0.996974	−	0.0777408i	$-0.0247706\pi$
$991$	13.5730	+	23.5092i	0.431161	+	0.746793i	−0.565812	+	0.824534i	$0.691437\pi$
$992$	−3.91416	+	6.77953i	−0.124275	+	0.215250i
$993$	−2.65082			−0.0841213
$994$	−5.95783	+	6.39056i	−0.188971	+	0.202696i
$995$	−8.95805			−0.283989
$996$	1.18227	−	2.04776i	0.0374618	−	0.0648858i
$997$	−25.4005	−	43.9949i	−0.804441	−	1.39333i	−0.916668	−	0.399650i	$-0.869132\pi$
$997$	−25.4005	−	43.9949i	−0.804441	−	1.39333i	0.112227	−	0.993683i	$-0.464202\pi$
$998$	−4.33300	−	7.50497i	−0.137159	−	0.237566i
$999$	−18.1252	+	31.3938i	−0.573456	+	0.993256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.h.170.3		12
7.2	even	3		8281.2.a.bz.1.4		6
7.4	even	3	inner	1183.2.e.h.508.3		12
7.5	odd	6		8281.2.a.ca.1.4		6
13.3	even	3		91.2.g.b.9.3	✓	12
13.9	even	3		91.2.h.b.16.4	yes	12
13.12	even	2		1183.2.e.g.170.4		12
39.29	odd	6		819.2.n.d.100.4		12
39.35	odd	6		819.2.s.d.289.3		12
91.3	odd	6		637.2.h.l.165.4		12
91.9	even	3		637.2.f.k.393.3		12
91.12	odd	6		8281.2.a.cf.1.3		6
91.16	even	3		637.2.f.k.295.3		12
91.25	even	6		1183.2.e.g.508.4		12
91.48	odd	6		637.2.h.l.471.4		12
91.51	even	6		8281.2.a.ce.1.3		6
91.55	odd	6		637.2.g.l.373.3		12
91.61	odd	6		637.2.f.j.393.3		12
91.68	odd	6		637.2.f.j.295.3		12
91.74	even	3		91.2.g.b.81.3	yes	12
91.81	even	3		91.2.h.b.74.4	yes	12
91.87	odd	6		637.2.g.l.263.3		12
273.74	odd	6		819.2.n.d.172.4		12
273.263	odd	6		819.2.s.d.802.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.3	✓	12	13.3	even	3
91.2.g.b.81.3	yes	12	91.74	even	3
91.2.h.b.16.4	yes	12	13.9	even	3
91.2.h.b.74.4	yes	12	91.81	even	3
637.2.f.j.295.3		12	91.68	odd	6
637.2.f.j.393.3		12	91.61	odd	6
637.2.f.k.295.3		12	91.16	even	3
637.2.f.k.393.3		12	91.9	even	3
637.2.g.l.263.3		12	91.87	odd	6
637.2.g.l.373.3		12	91.55	odd	6
637.2.h.l.165.4		12	91.3	odd	6
637.2.h.l.471.4		12	91.48	odd	6
819.2.n.d.100.4		12	39.29	odd	6
819.2.n.d.172.4		12	273.74	odd	6
819.2.s.d.289.3		12	39.35	odd	6
819.2.s.d.802.3		12	273.263	odd	6
1183.2.e.g.170.4		12	13.12	even	2
1183.2.e.g.508.4		12	91.25	even	6
1183.2.e.h.170.3		12	1.1	even	1	trivial
1183.2.e.h.508.3		12	7.4	even	3	inner
8281.2.a.bz.1.4		6	7.2	even	3
8281.2.a.ca.1.4		6	7.5	odd	6
8281.2.a.ce.1.3		6	91.51	even	6
8281.2.a.cf.1.3		6	91.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.134063 - 0.232203i) q^{2} +(0.571504 + 0.989875i) q^{3} +(0.964054 + 1.66979i) q^{4} +(1.28088 - 2.21854i) q^{5} +0.306470 q^{6} +(-2.57801 - 0.594848i) q^{7} +1.05323 q^{8} +(0.846765 - 1.46664i) q^{9} +(-0.343436 - 0.594848i) q^{10} +(-1.97300 - 3.41734i) q^{11} +(-1.10192 + 1.90859i) q^{12} +(-0.483741 + 0.518876i) q^{14} +2.92811 q^{15} +(-1.78691 + 3.09502i) q^{16} +(-0.392550 - 0.679916i) q^{17} +(-0.227039 - 0.393243i) q^{18} +(3.74764 - 6.49110i) q^{19} +4.93934 q^{20} +(-0.884522 - 2.89187i) q^{21} -1.05802 q^{22} +(3.97759 - 6.88938i) q^{23} +(0.601923 + 1.04256i) q^{24} +(-0.781294 - 1.35324i) q^{25} +5.36475 q^{27} +(-1.49207 - 4.87821i) q^{28} +2.35173 q^{29} +(0.392550 - 0.679916i) q^{30} +(1.27718 + 2.21215i) q^{31} +(1.53234 + 2.65409i) q^{32} +(2.25516 - 3.90605i) q^{33} -0.210505 q^{34} +(-4.62182 + 4.95751i) q^{35} +3.26531 q^{36} +(-3.37858 + 5.85187i) q^{37} +(-1.00484 - 1.74043i) q^{38} +(1.34905 - 2.33663i) q^{40} -2.43747 q^{41} +(-0.790083 - 0.182303i) q^{42} -2.24946 q^{43} +(3.80416 - 6.58900i) q^{44} +(-2.16920 - 3.75717i) q^{45} +(-1.06649 - 1.84722i) q^{46} +(-0.658276 + 1.14017i) q^{47} -4.08491 q^{48} +(6.29231 + 3.06705i) q^{49} -0.418969 q^{50} +(0.448688 - 0.777151i) q^{51} +(-4.63977 - 8.03632i) q^{53} +(0.719212 - 1.24571i) q^{54} -10.1087 q^{55} +(-2.71523 - 0.626509i) q^{56} +8.56716 q^{57} +(0.315279 - 0.546079i) q^{58} +(4.48335 + 7.76540i) q^{59} +(2.82286 + 4.88933i) q^{60} +(-4.72273 + 8.18002i) q^{61} +0.684890 q^{62} +(-3.05540 + 3.27732i) q^{63} -6.32592 q^{64} +(-0.604665 - 1.04731i) q^{66} +(0.676281 + 1.17135i) q^{67} +(0.756879 - 1.31095i) q^{68} +9.09284 q^{69} +(0.531538 + 1.73782i) q^{70} +12.3162 q^{71} +(0.891834 - 1.54470i) q^{72} +(-0.384295 - 0.665619i) q^{73} +(0.905882 + 1.56903i) q^{74} +(0.893026 - 1.54677i) q^{75} +14.4517 q^{76} +(3.05363 + 9.98358i) q^{77} +(-3.09642 + 5.36316i) q^{79} +(4.57763 + 7.92868i) q^{80} +(0.525682 + 0.910507i) q^{81} +(-0.326774 + 0.565989i) q^{82} -1.07292 q^{83} +(3.97609 - 4.26489i) q^{84} -2.01123 q^{85} +(-0.301568 + 0.522332i) q^{86} +(1.34402 + 2.32792i) q^{87} +(-2.07801 - 3.59923i) q^{88} +(-3.83149 + 6.63634i) q^{89} -1.16324 q^{90} +15.3384 q^{92} +(-1.45983 + 2.52850i) q^{93} +(0.176501 + 0.305708i) q^{94} +(-9.60052 - 16.6286i) q^{95} +(-1.75148 + 3.03365i) q^{96} -2.37202 q^{97} +(1.55574 - 1.04992i) q^{98} -6.68267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + q^{3} - 4 q^{4} + q^{5} + 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{14} + 4 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} - 9 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + q^3 - 4 * q^4 + q^5 + 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^14 + 4 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 - q^19 + 2 * q^20 - 9 * q^21 + 10 * q^22 - q^23 - 11 * q^24 + 7 * q^25 - 8 * q^27 + 8 * q^28 - 6 * q^29 - 5 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 + 32 * q^34 - 28 * q^35 + 42 * q^36 - 13 * q^37 - 17 * q^38 - 5 * q^40 + 16 * q^41 - 52 * q^42 + 22 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 - 42 * q^48 + 6 * q^49 - 12 * q^50 - 20 * q^51 - 2 * q^53 - 18 * q^54 - 18 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 + 13 * q^59 + 20 * q^60 - 5 * q^61 - 10 * q^62 + 8 * q^63 - 30 * q^64 + 18 * q^66 - 11 * q^67 + 29 * q^68 - 46 * q^69 - 39 * q^70 - 12 * q^71 + 25 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 + 18 * q^76 + 11 * q^77 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 + 41 * q^84 + 2 * q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 + 54 * q^92 - 7 * q^93 + 45 * q^94 - 6 * q^95 + 19 * q^96 + 70 * q^97 - 82 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more